Displaying similar documents to “Degenerations for modules over representation-finite selfinjective algebras”

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...

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...

Substructures of algebras with weakly non-negative Tits form.

José Antonio de la Peña, Andrzej Skowronski (2007)

Extracta Mathematicae

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Let A = kQ/I be a finite dimensional basic algebra over an algebraically closed field k presented by its quiver Q with relations I. A fundamental problem in the representation theory of algebras is to decide whether or not A is of tame or wild type. In this paper we consider triangular algebras A whose quiver Q has no oriented paths. We say that A is essentially sincere if there is an indecomposable (finite dimensional) A-module whose support contains all extreme vertices of Q. We prove...