Finiteness of the strong global dimension of radical square zero algebras.
type: Item
instance of: scholarly article
title: Finiteness of the strong global dimension of radical square zero algebras.
zbMATH Open document ID: 1061.16011
DOI: 10.2478/BF02475954
author: Otto Kerner
author: Andrzej Skowroński
author: Dan Zacharia
author: Kunio Yamagata
published in: Central European Journal of Mathematics
publication date: 2004-02-23T00:00:00Z
review text: The strong global dimension of a finite-dimensional associative algebra \(A\) is the maximum of the widths of indecomposable bounded differential complexes of finite-dimensional projective \(A\)-modules. The authors show that for a radical square zero algebra \(A\) over an algebraically closed field one has that \(A\) has finite strong global dimension if and only if \(A\) is piecewise hereditary and discuss some other results concerning the finiteness of the strong global dimension.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 2046457
zbMATH Keywords: strong global dimension
zbMATH Keywords: repetitive algebras
zbMATH Keywords: differential complexes
zbMATH Keywords: radical square zero algebras
zbMATH Keywords: piecewise hereditary algebras
MaRDI profile type: Publication
cites work: Domestic trivial extensions of simply connected algebras
cites work: Algebras with cycle-finite derived categories
cites work: Q4314802
cites work: Covering spaces in representation-theory
cites work: On Galois coverings of tame algebras
cites work: Galois coverings of representation-infinite algebras
cites work: Self-injective algebras of wild tilted type
cites work: Q3937542
cites work: Graphs with Relations, Coverings and Group-Graded Algebras
cites work: On the derived category of a finite-dimensional algebra
cites work: A characterization of hereditary categories with tilting object
cites work: Tilting in abelian categories and quasitilted algebras
cites work: Piecewise hereditary algebras
cites work: Piecewise Hereditary Algebras
cites work: Trivial Extensions of Tilted Algebras
cites work: Selfinjective algebras of wild canonical type
cites work: Polynomial growth trivial extensions of simply connected algebras
cites work: Tame algebras and integral quadratic forms
cites work: On the quiver with relations of a repetitive algebra
cites work: Generalization of Yamagata's theorem on trivial extensions
cites work: Q3784273
cites work: Tame quasi-tilted algebras
cites work: Q3931576
full work available at URL: https://doi.org/10.2478/bf02475954
OpenAlex ID: W1976787206
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description: scientific article; zbMATH DE number 2046457