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  • 1. Barnsley, Michael
    et al.
    Hutchinson, John E.
    Stenflo, Örjan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    V-variable fractals: dimension results2012In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 24, no 3, p. 445-470Article in journal (Refereed)
    Abstract [en]

    The families of V-variable fractals for V = 1, 2, ... , together with their natural probability distributions, interpolate between the corresponding families of random homogeneous fractals and of random recursive fractals. We investigate certain random V x V matrices associated with these fractals and use them to compute the almost sure Hausdorff dimension of V-variable fractals satisfying the uniform open set condition.

  • 2.
    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.

  • 3.
    Dubsky, Brendan Frisk
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Guo, Xiangqian
    Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China.
    Yao, Yufeng
    Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China.
    Zhao, Kaiming
    Hebei Normal Teachers Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Hebei, Peoples R China;Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada.
    Simple modules over the Lie algebras of divergence zero vector fields on a torus2019In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 31, no 3, p. 727-741Article in journal (Refereed)
    Abstract [en]

    Let n >= 2 be an integer, S-n the Lie algebra of divergence zero vector fields on an n-dimensional torus, and K-n the Weyl algebra over the Laurent polynomial algebra A(n) = C[x(1)(+/- 1), x(2)(+/- 1), . . . , x(n)(+/- 1)]. For any sln-module V and any module P over K-n, we define an S-n-module structure on the tensor product P circle times V. In this paper, necessary and sufficient conditions for the S-n-modules P circle times V to be simple are given, and an isomorphism criterion for nonminuscule S-n-modules is provided. More precisely, all nonminuscule S-n-modules are simple, and pairwise nonisomorphic. For minuscule S-n-modules, minimal and maximal submodules are concretely determined.

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