Displaying similar documents to “Actions of parabolic subgroups in GL_n on unipotent normal subgroups and quasi-hereditary algebras”

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

Thomas Brüstle, Lutz Hille (2000)

Colloquium Mathematicae

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Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent...

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 ∪ ℛ A co-finite in ind A, quasi-tilted...

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.

Partial flag varieties and preprojective algebras

Christof Geiß, Bernard Leclerc, Jan Schröer (2008)

Annales de l’institut Fourier

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Let Λ be a preprojective algebra of type A , D , E , and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ -module, and we introduce a mutation operation between complete rigid modules in Sub Q . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to  G .

On a family of vector space categories

Grzegorz Bobiński, Andrzej Skowroński (2003)

Open Mathematics

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In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten...