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Displaying similar documents to “Tame minimal non-polynomial growth simply connected algebras”

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...

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 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...