Tilted symmetric orders are symmetric orders
type: Item
instance of: scholarly article
title: Tilted symmetric orders are symmetric orders
zbMATH Open document ID: 0932.16011
published in: Archiv der Mathematik
publication date: 2000-03-13T00:00:00Z
review text: Let \(R\) be a Dedekind domain with quotient field \(K\), and \(\Lambda\) an \(R\)-order, that is, an \(R\)-algebra with \(_R\Lambda\) finitely generated and projective such that \(K\otimes_R\Lambda\) is semisimple. \(\Lambda\) is said to be symmetric if there is a bimodule isomorphism \(_\Lambda\Lambda_\Lambda\cong\Hom_R(\Lambda,R)\). It is proved that if \(\Lambda\) is derived equivalent to an \(R\)-algebra \(\Gamma\), then \(\Gamma\) is again a symmetric \(R\)-order. This improves a result of \textit{J. Rickard} [J. Lond. Math. Soc., II. Ser. 43, No. 1, 37-48 (1991; Zbl 0683.16030)].
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 1346237
zbMATH Keywords: Dedekind domains
zbMATH Keywords: bimodule isomorphisms
zbMATH Keywords: derived equivalences
zbMATH Keywords: symmetric orders
author: Alexander Zimmermann
reviewed by: Wolfgang Rump
MaRDI profile type: Publication
full work available at URL: s000130050014
OpenAlex ID: W2007074579
DOI: 10.1007/S000130050014
description: scientific article; zbMATH DE number 1346237