Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras

Thomas Brüstle; Lutz Hille

Displaying similar documents to “Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras”

Actions of parabolic subgroups in GL_n on unipotent normal subgroups and quasi-hereditary algebras

Thomas Brüstle, Lutz Hille (2000)

Colloquium Mathematicae

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Let R be a parabolic subgroup in $G L_{n}$ . It acts on its unipotent radical $R_{u}$ and on any unipotent normal subgroup U via conjugation. Let Λ be the path algebra $k_{t}$ of a directed Dynkin quiver of type with t vertices and B a subbimodule of the radical of Λ viewed as a Λ-bimodule. Each parabolic subgroup R is the group of automorphisms of an algebra Λ(d), which is Morita equivalent to Λ. The action of R on U can be described using matrices over the bimodule B. The advantage of this description...

A brief review of abelian categorifications.

Khovanov, Mikhail, Mazorchuk, Volodymyr, Stroppel, Catharina (2009)

Theory and Applications of Categories [electronic only]

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A remark on the Morita theorem for operads

Alexandru E. Stanculescu (2011)

Archivum Mathematicum

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We extend a result of M. M. Kapranov and Y. Manin concerning the Morita theory for linear operads. We also give a cyclic operad version of their result.

Serre functors for Lie algebras and superalgebras

Volodymyr Mazorchuk, Vanessa Miemietz (2012)

Annales de l’institut Fourier

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We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category $𝒪$ associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to classical Lie superalgebras in many cases. Along the way we prove that category $𝒪$ and its parabolic generalizations for classical Lie superalgebras are categories with full projective functors. As an application we prove that in many cases the endomorphism algebra...

Componentwise injective models of functors to DGAs

Marek Golasiński (1997)

Colloquium Mathematicae

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The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.

Internal crossed modules.

Janelidze, G. (2003)

Georgian Mathematical Journal

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Doubles for monoidal categories.

Pastro, Craig, Street, Ross (2008)

Theory and Applications of Categories [electronic only]

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Mackey functors on compact closed categories.

Panchadcharam, E., Street, R. (2007)

Journal of Homotopy and Related Structures

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On artin algebras with almost all indecomposable modules of projective or injective dimension at most one

Andrzej Skowroński (2003)

Open Mathematics

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Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote $ℒ_{A}$ to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by $ℛ_{A}$ the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with $ℒ_{A} \cup ℛ_{A}$ co-finite in ind A, quasi-tilted...