Derived equivalences and Cohen-Macaulay Auslander algebras
type: Item
instance of: scholarly article
title: Derived equivalences and Cohen-Macaulay Auslander algebras
zbMATH Open document ID: 1330.18018
author: Shengyong Pan
author: Xiaojin Zhang
published in: Frontiers of Mathematics in China
publication date: 2015-11-19T00:00:00Z
review text: The paper under review is a generalisation of an earlier paper of the first author [J. Pure Appl. Algebra 216, No. 2, 355--363 (2012; Zbl 1260.16014)]. It is shown that if two Artin algebras of finite Cohen-Macaulay type are related via a standard derived equivalence (i.e.\ induced by a two-sided tilting complex), then their associated Cohen-Macaulay Auslander algebras (i.e.\ the endomorphism algebra of an additive generator for the Gorenstein projective modules) are derived equivalent. The earlier paper proved this in the case of Gorenstein algebras, without the restriction on the form of the derived equivalence. This shows that the Gorenstein projective conjecture is invariant under standard derived equivalence.
reviewed by: Pieter Belmans
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 18G15
zbMATH DE Number: 6511736
zbMATH Keywords: standard derived equivalence
zbMATH Keywords: Cohen-Macaulay Auslander algebra
zbMATH Keywords: Gorenstein projective conjecture, finite Cohen-Macaulay type
MaRDI profile type: Publication
full work available at URL: s11464-015-0437-3
OpenAlex ID: W2760470956
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DOI: 10.1007/S11464-015-0437-3
description: scientific article; zbMATH DE number 6511736