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Dlab's theorem and tilting modules for stratified algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 314, no 2, 507-537 p.Article in journal (Refereed) Published
Abstract [en]

In the first part of the paper we give a characterization for an associative algebra to be standardly stratified in the sense of Cline, Parshall and Scott, generalizing a theorem of V. Dlab. In the second part of the paper we construct characteristic tilting modules for standardly stratified algebras and use them to estimate the finitistic dimension of such algebras. These tilting modules give rise to the Ringel duality concept for stratified algebras. We also define and investigate a generalization of the notion of properly stratified algebras to the above setup.

Place, publisher, year, edition, pages
2007. Vol. 314, no 2, 507-537 p.
Keyword [en]
Dlab's theorem, Finitistic dimension, Ringel dual, Stratified algebras
National Category
URN: urn:nbn:se:uu:diva-95661DOI: 10.1016/j.jalgebra.2006.08.041ISI: 000249038300001OAI: oai:DiVA.org:uu-95661DiVA: diva2:169966
Available from: 2007-05-03 Created: 2007-05-03 Last updated: 2011-01-25Bibliographically approved
In thesis
1. On Stratified Algebras and Lie Superalgebras
Open this publication in new window or tab >>On Stratified Algebras and Lie Superalgebras
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis, consisting of three papers and a summary, studies properties of stratified algebras and representations of Lie superalgebras.

In Paper I we give a characterization when the Ringel dual of an SSS-algebra is properly stratified.

We show that for an SSS-algebra, whose Ringel dual is properly stratified, there is a (generalized) tilting module which allows one to compute the finitistic dimension of the SSS-algebra, and moreover, it gives rise to a new covariant Ringel-type duality.

In Paper II we give a characterization of standardly stratified algebras in terms of certain filtrations of (left or right) projective modules, generalizing the corresponding theorem of V. Dlab. We extend the notion of Ringel duality to standardly stratified algebras and estimate their finitistic dimension in terms of endomorphism algebras of standard modules.

Paper III deals with the queer Lie superalgebra and the corresponding BGG-category O. We show that the typical blocks correspond to standardly stratified algebras, and we generalize Kostant's Theorem to the queer Lie superalgebra.

Place, publisher, year, edition, pages
Uppsala: Matematiska institutionen, 2007. 17 p.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 48
Algebra and geometry, Stratified algebras, Lie Superalgebras, Properly stratified algebras, Quasi-hereditary algebras, the queer Lie superalgebra, Kostant's Theorem, Algebra och geometri
urn:nbn:se:uu:diva-7781 (URN)978-91-506-1927-0 (ISBN)
Public defence
2007-05-29, MIC2247, House 2, Polacksbacken, Uppsala, 13:15
Available from: 2007-05-03 Created: 2007-05-03Bibliographically approved

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