A note on standard equivalences
type: Item
instance of: scholarly article
title: A note on standard equivalences
zbMATH Open document ID: 1352.13010
author: Xiao-Wu Chen
published in: Bulletin of the London Mathematical Society
publication date: 2016-10-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1504.06013
Mathematics Subject Classification ID: 13D09
Mathematics Subject Classification ID: 16E35
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 6645451
MaRDI profile type: Publication
OpenAlex ID: W2963447475
arXiv ID: 1504.06013
cites work: Koszul duality and semisimplicity of Frobenius
cites work: Classification of discrete derived categories
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cites work: On triangulated orbit categories
cites work: Ampleness of two-sided tilting complexes
cites work: Derived Picard groups of finite-dimensional hereditary algebras
cites work: Derived Equivalences As Derived Functors
cites work: Tame algebras and integral quadratic forms
cites work: Representation theory. A homological algebra point of view.
DOI: 10.1112/BLMS/BDW038
review text: A finite dimensional algebra \(A\) over a field is said to be triangular if its Gabriel quiver has no oriented cycles. If \(A\) is derived equivalent to a triangular algebra, it is proved that any derived equivalence (of bounded derived categories of finitely generated modules) between \(A\) and another finite dimensional algebra is standard. This means that the equivalence is obtained by tensoring with a two-sided tilting complex. Examples of triangular algebras are piecewise hereditary ones. However, it should be noted that the triangular property is not invariant under derived equivalence.
reviewed by: Wolfgang Rump
description: scientific article; zbMATH DE number 6645451