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  • 1. Andersen, Henning Haahr
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Category O for quantum groups2015In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 17, no 2, p. 405-431Article in journal (Refereed)
    Abstract [en]

    We study the BGG-categories O-q associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for O and for finite-dimensional U-q-modules we are able to determine all irreducible characters as well as the characters of all indecomposable tilting modules in O-q. As a consequence, we also recover the known result that the generic quantum case behaves like the classical category O.

  • 2. Baur, Karin
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras2012In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 372, p. 85-107Article in journal (Refereed)
    Abstract [en]

    We study certain types of ideals in the standard Borel subalgebra of an untwisted affine Lie algebra. We classify these ideals in terms of the root combinatorics and give an explicit formula for the number of such ideals in type A. The formula involves various aspects of combinatorics of Dyck paths and leads to a new interesting integral sequence.

  • 3. Britten, Daniel
    et al.
    Khomenko, Oleksandr
    Lemire, Francis
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    Complete reducibility of torsion free C_n-modules of finite degree2004In: Journal of Algebra, Vol. 276, p. 129-142Article in journal (Refereed)
  • 4. Cheng, Shun-Jen
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Wang, Weiqiang
    Equivalence of Blocks for the General Linear Lie Superalgebra2013In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 103, no 12, p. 1313-1327Article in journal (Refereed)
    Abstract [en]

    We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category for a general linear Lie superalgebra to an integral block of for (possibly a direct sum of) general linear Lie superalgebras. We also establish indecomposability of blocks of .

  • 5.
    Coulembier, Kevin
    et al.
    Univ Ghent, Dept Math Anal, Krijgslaan 281, B-9000 Ghent, Belgium..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Dualities and derived equivalences for category O2017In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 219, no 2, p. 661-706Article in journal (Refereed)
    Abstract [en]

    We determine the Ringel duals for all blocks in the parabolic versions of the BGG category associated to a reductive finite-dimensional Lie algebra. In particular, we find that, contrary to the original category and the specific previously known cases in the parabolic setting, the blocks are not necessarily Ringel self-dual. However, the parabolic category as a whole is still Ringel self-dual. Furthermore, we use generalisations of the Ringel duality functor to obtain large classes of derived equivalences between blocks in parabolic and original category . We subsequently classify all derived equivalence classes of blocks of category in type A which preserve the Koszul grading.

  • 6. Coulembier, Kevin
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules2015In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 11, article id 016Article in journal (Refereed)
    Abstract [en]

    We prove that the categories of Gelfand-Zeitlin modules of g = gl(n), and Whittaker modules associated with a semi-simple complex finite-dimensional algebra g are extension full in the category of all g-modules. This is used to estimate and in some cases determine the global dimension of blocks of the categories of Gelfand-Zeitlin and Whittaker modules.

  • 7.
    Coulembier, Kevin
    et al.
    Univ Ghent, Dept Math Anal, B-9000 Ghent, Belgium..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Some homological properties of category O. III2015In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 283, p. 204-231Article in journal (Refereed)
    Abstract [en]

    We prove that thick category O associated to a semi-simple complex finite dimensional Lie algebra is extension full in the category of all modules. We also prove the weak Alexandru conjecture both for regular blocks of thick category O and the associated categories of Harish-Chandra bimodules, but disprove it for singular blocks.

  • 8.
    Coulembier, Kevin
    et al.
    Univ Sydney, Sch Math & Stat;Univ Ghent, Dept Math Anal.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Some homological properties of category O. IV2017In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 29, no 5, p. 1083-1124Article in journal (Refereed)
    Abstract [en]

    We study projective dimension and graded length of structural modules in parabolic-singular blocks of the BGG category O. Some of these are calculated explicitly, others are expressed in terms of two functions. We also obtain several partial results and estimates for these two functions and relate them to monotonicity properties for quasi-hereditary algebras. The results are then applied to study blocks of O in the context of Guichardet categories, in particular, we show that blocks of O are not always weakly Guichardet.

  • 9. Drozd, Yuriy
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Representation type of H-infinity(lambda)mu(1)2006In: Quarterly Journal of Mathematics, ISSN 0033-5606, E-ISSN 1464-3847, Vol. 57, no 3, p. 319-338Article in journal (Refereed)
    Abstract [en]

    For a semi-simple finite-dimensional complex Lie algebra, we classify the representation type of the associative algebras associated with the categories H-infinity(lambda)mu(1) of Harish-Chandra bimodules for g.

  • 10.
    Dubsky, Brendan Frisk
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Lu, Rencai
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Zhao, Kaiming
    Category O for the Schrodinger algebra2014In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 460, p. 17-50Article in journal (Refereed)
    Abstract [en]

    We study category O for the (centrally extended) Schrodinger algebra. We determine the quivers for all blocks and relations for blocks of nonzero central charge. We also describe the quiver and relations for the finite dimensional part of O. We use this to determine the center of the universal enveloping algebra and annihilators of Verma modules. Finally, we classify primitive ideals of the universal enveloping algebra which intersect the center of the centrally extended Schrodinger algebra trivially.

  • 11.
    Frisk, Anders
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Properly stratified algebras and tilting2003Report (Other scientific)
  • 12.
    Frisk, Anders
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    Properly stratified algebras and tilting2006In: Proc. London Math. Soc., ISSN 0024-6115, Vol. 92, no 1, p. 29-Article in journal (Refereed)
    Abstract [en]

    We study the properties of tilting modules in the context of properly

    stratified algebras. In particular, we answer the question when the

    Ringel dual of a properly stratified algebra is properly stratified

    itself, and show that the class of properly stratified algebras for

    which the characteristic tilting and cotilting modules coincide is

    closed under taking the Ringel dual. Studying stratified algebras,

    whose Ringel dual is properly stratified, we discover a new Ringel-type

    duality for such algebras, which we call the two-step duality. This

    duality arises from the existence of a new (generalized) tilting module

    for stratified algebras with properly stratified Ringel dual. We

    show that this new tilting module has a lot of interesting properties,

    for instance, its projective dimension equals the projectively defined

    finitistic dimension of the original algebra, it guarantees that the

    category of modules of finite projective dimension is contravariantly

    finite, and, finally, it allows one to compute the finitistic dimension of

    the original algebra in terms of the projective dimension of the

    characteristic tilting module.

  • 13. Futorny, Vyacheslav
    et al.
    Grantcharov, Dimitar
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Weight Modules over Infinite Dimensional Weyl Algebras2014In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 142, no 9, p. 3049-3057Article in journal (Refereed)
    Abstract [en]

    We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from this a description of blocks of the category of weight modules by quivers and relations. As a corollary we establish Koszulity for all blocks.

  • 14. Ganyuhskin, Olexandr
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Classical finite transformation semigroups: an introduction2009Book (Other (popular science, discussion, etc.))
  • 15. Ganyushkin, Olexandr
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Combinatorics and distributions of partial injections2003Report (Other scientific)
  • 16.
    Greenstein, Jacob
    et al.
    Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Koszul Duality for Semidirect Products and Generalized Takiff Algebras2017In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 20, no 3, p. 675-694Article in journal (Refereed)
    Abstract [en]

    We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with its degree zero part and a graded module algebra for the latter. In particular, this applies to graded representations of the universal enveloping algebra of the Takiff Lie algebra (or the truncated current algebra) and its (super)analogues, and also to semidirect products of quantum groups with braided symmetric and exterior module algebras in case the latter are flat deformations of classical ones.

  • 17. Grensing, Anna-Louise
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Categorification of the Catalan monoid2014In: Semigroup Forum, ISSN 0037-1912, E-ISSN 1432-2137, Vol. 89, no 1, p. 155-168Article in journal (Refereed)
    Abstract [en]

    We construct a finitary additive 2-category whose Grothendieck ring is isomorphic to the semigroup algebra of the monoid of order-decreasing and order-preserving transformations of a finite chain.

  • 18.
    Grensing, Anna-Louise
    et al.
    Univ Bielefeld, Fac Math, POB 100 131, D-33501 Bielefeld, Germany..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Finitary 2-categories associated with dual projection functors2017In: Communications in Contemporary Mathematics, ISSN 0219-1997, Vol. 19, no 3, article id 1650016Article in journal (Refereed)
    Abstract [en]

    We study finitary 2-categories associated to dual projection functors for finite-dimensional associative algebras. In the case of path algebras of admissible tree quivers (which includes all Dynkin quivers of type A), we show that the monoid generated by dual projection functors is the Hecke-Kiselman monoid of the underlying quiver and also obtain a presentation for the monoid of indecomposable subbimodules of the identity bimodule.

  • 19.
    Janson, Svante
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Some remarks on the combinatorics of IS_n2005In: Semigroup Forum 70, no 3, p. 391-405Article in journal (Refereed)
  • 20.
    Janson, Svante
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Some remarks on the combinatorics of ISn2004Report (Other scientific)
  • 21. Khomenko, Oleksander
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    On Arkhipov's and Enright's functors2003Report (Other scientific)
  • 22. Khomenko, Oleksandr
    et al.
    Koenig, Steffen
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Finitistic dimension and tilting modules for stratified algebras2003Report (Other scientific)
  • 23. Khovanov, Mikhail
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
    Stroppel, Catharina
    A brief review of abelian categorifications2009In: Theory and Applications of Categories, ISSN 1201-561X, E-ISSN 1201-561X, Vol. 22, no 19, p. 479-508Article in journal (Refereed)
  • 24. Khovanov, Mikhail
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Stroppel, Catharina
    A categorification of integral Specht modules2006Report (Other (popular scientific, debate etc.))
  • 25.
    Kildetoft, Tobias
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Special Modules Over Positively Based Algebras2016In: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 21, p. 1171-1192Article in journal (Refereed)
    Abstract [en]

    We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the Kazhdan-Lusztig basis, this agrees with Lusztig's notion of a special module introduced in [Lu2].

  • 26. Kudryavsteva, Ganna
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Partialization of categories and inverse braid-permutation monoid2006Report (Other (popular scientific, debate etc.))
  • 27. Kudryavtseva, Ganna
    et al.
    Maltcev, Victor
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    L- and R- cross-sections in the Brauer semigroup2006In: Semigroup Forum, Vol. 72, p. 223-248Article in journal (Refereed)
  • 28. Kudryavtseva, Ganna
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    On Kiselman's semigroup2009In: Yokohama Mathematical Journal, ISSN 0044-0523, Vol. 55, no 1, p. 21-46Article in journal (Refereed)
  • 29. Kudryavtseva, Ganna
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    On multisemigroups2015In: Portugaliae Mathematica, ISSN 0032-5155, E-ISSN 1662-2758, Vol. 72, no 1, p. 47-80Article in journal (Refereed)
    Abstract [en]

    Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for multisemigroups. Special attention is paid to simple and nilpotent multisemigroups. We also show that "almost all'' randomly chosen multivalued binary operations define multisemigroups.

  • 30. Kudryavtseva, Ganna
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    On presentations of Brauer-type monoids2006In: Central Europian Journal of Mathematics, Vol. 4, no 3, p. 413-434Article in journal (Refereed)
  • 31. Kudryavtseva, Ganna
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    On three approaches to conjugacy in semigroups2009In: Semigroup Forum, ISSN 0037-1912, E-ISSN 1432-2137, Vol. 78, no 1, p. 14-20Article in journal (Refereed)
    Abstract [en]

    We compare three approaches to the notion of conjugacy for semigroups, the first one via the transitive closure of the uvvu relation, the second one via an action of inverse semigroups on themselves by partial transformations, and the third one via characters of finite-dimensional representations.

  • 32. Lu, Rencai
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Zhao, Kaiming
    On simple modules over conformal Galilei algebras2014In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 218, no 10, p. 1885-1899Article in journal (Refereed)
    Abstract [en]

    We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules over the conformal Galilei algebras. This can be viewed as an analogue of oscillator representations. We use oscillator representations to describe the structure of simple highest weight modules over conformal Galilei algebras. We classify simple weight modules with finite dimensional weight spaces over finite dimensional Heisenberg algebras and use this classification and properties of oscillator representations to classify simple weight modules with finite dimensional weight spaces over conformal Galilei algebras. 

  • 33. Lu, Rencai
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Zhao, Kaiming
    Simple weight modules over weak generalized Weyl algebras2015In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, no 8, p. 3427-3444Article in journal (Refereed)
    Abstract [en]

    In this paper we address the problem of classification of simple weight modules over weak generalized Weyl algebras of rank one. The principal difference between weak generalized Weyl algebras and generalized Weyl algebras is that weak generalized Weyl algebras are defined using an endomorphism rather than an automorphism of a commutative ring R. We reduce classification of simple weight modules over weak generalized Weyl algebras to description of the dynamics of the action of the above mentioned endomorphism on the set of maximal ideals. We also describe applications of our results to the study of generalized Heisenberg algebras.

  • 34. Maltcev, Victor
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Presentation of the singular part of the Brauer monoid2006Report (Other (popular scientific, debate etc.))
  • 35.
    Martin, Paul
    et al.
    Univ Leeds, Dept Pure Math, Leeds LS2 9JT, W Yorkshire, England..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Fiat categorification of the symmetric inverse semigroup ISn and the semigroup Fn*2018In: Semigroup Forum, ISSN 0037-1912, E-ISSN 1432-2137, Vol. 96, no 1, p. 142-159Article in journal (Refereed)
    Abstract [en]

    Starting from the symmetric group , we construct two fiat 2-categories. One of them can be viewed as the fiat "extension" of the natural 2-category associated with the symmetric inverse semigroup (considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the symmetric inverse semigroup. The other 2-category can be viewed as the fiat "extension" of the 2-category associated with the maximal factorizable subsemigroup of the dual symmetric inverse semigroup (again, considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the maximal factorizable subsemigroup of the dual symmetric inverse semigroup.

  • 36. Martin, Paul
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    On the Representation Theory of Partial Brauer Algebras2014In: Quarterly Journal of Mathematics, ISSN 0033-5606, E-ISSN 1464-3847, Vol. 65, no 1, p. 225-247Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the partial Brauer C-algebras R-n(delta, delta'), where n is an element of N and delta, delta' is an element of C. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction Rn-1 (sic) R-n. We also determine the corresponding decomposition matrix and the Cartan decomposition matrix.

  • 37. Martin, Paul
    et al.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Partitioned binary relations2013In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 113, no 1, p. 30-52Article in journal (Refereed)
    Abstract [en]

    We define the category of partitioned binary relations and show that it contains many classical diagram categories, including categories of binary relations, maps, injective maps, partitions, (oriented) Brauer diagrams and (oriented) Temperley-Lieb diagrams. We construct a one-parameter deformation of the category of partitioned binary relations and show that it gives rise to classical one-parameter deformations of partition, Brauer and Temperley-Lieb categories. Finally, we describe a factorization of partitioned binary relations into a product of certain idempotents and pairs of usual binary relations.

  • 38.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    A twisted approach to Kostant's problem2005In: Glasgow Mathematical Journal, no 47, p. 549-561Article in journal (Refereed)
  • 39.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    A twisted approach to Kostant's problem2005Report (Other scientific)
  • 40.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    Applications of the category of linear complexes of tilting modules associated with the category O2005Report (Other scientific)
  • 41.
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Combinatorial Gelfand Models for Semisimple Diagram Algebras2013In: Milan Journal of Mathematics, ISSN 1424-9286, E-ISSN 1424-9294, Vol. 81, no 2, p. 385-396Article in journal (Refereed)
    Abstract [en]

    We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebras, their partial analogues, walled Brauer algebras, their partial analogues, Temperley-Lieb algebras, their partial analogues, walled Temperley-Lieb algebras, their partial analogues, partition algebras and their Temperley-Lieb analogues.

  • 42.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    On finitistic dimension of stratified algebras2004Report (Other scientific)
  • 43.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    On finitistic dimension of stratified algebras2004In: Alg. Discrete Math., Vol. 3, no 3, p. 77-88Article in journal (Refereed)
  • 44.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    On quasicrystal Lie algebras2002In: Journal of Mathematical Physics, Vol. 43, p. 2791-2801Article in journal (Refereed)
  • 45.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    On simple mixed modules over the Virasoro algebra2004In: Mat. Studii, Vol. 22, no 2, p. 121-128Article in journal (Refereed)
  • 46.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Some homological properties of the category O2006Report (Other (popular scientific, debate etc.))
  • 47.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Stratified algebras arising in Lie theory2004In: Representations of finite-dimensional algebras and, Fields Institute , 2004, p. 245-260Chapter in book (Refereed)
  • 48.
    Mazorchuk, Volodymyr
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    Stratified algebras arising in Lie theory2004In: Fields Institute Communications, Vol. 40, p. 245-260Article in journal (Other (popular scientific, debate etc.))
  • 49.
    Mazorchuk, Volodymyr
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Drozd, Yuriy
    Koszul duality for extension algebras of standard modules2004Report (Other scientific)
  • 50.
    Mazorchuk, Volodymyr
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Drozd, Yuriy
    Representation type of2004Report (Other scientific)
12 1 - 50 of 92
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