On Hochschild cohomology of orders.
type: Item
instance of: scholarly article
title: On Hochschild cohomology of orders.
zbMATH Open document ID: 1051.16008
author: Katsunori Sanada
author: Nicole Snashall
author: Steffen Koenig
published in: Archiv der Mathematik
publication date: 2004-03-07T00:00:00Z
review text: For a class of tiled orders \(\Lambda\) close to hereditary orders, the authors calculate the Hochschild cohomology ring \(\text{HH}(\Lambda)\), generalizing previous work by \textit{K. Sanada} [J. Algebra 176, No. 3, 786-805 (1995; Zbl 0837.16010)]. They show first that \(\Lambda\) admits a two-sided projective resolution \[ \Lambda\rightarrowtail P_1\to P_0\twoheadrightarrow\Lambda. \] This gives \(\text{HH}(\Lambda)\cong R[x]/(ax)\), where \(a\) is an invariant of \(\Lambda\), and \(x\) is a cocycle of degree 2.
reviewed by: Wolfgang Rump
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 2051647
zbMATH Keywords: tiled orders
zbMATH Keywords: hereditary orders
zbMATH Keywords: Hochschild cohomology rings
MaRDI profile type: Publication
full work available at URL: s00013-003-0839-4
OpenAlex ID: W2093189805
DOI: 10.1007/S00013-003-0839-4
description: scientific article; zbMATH DE number 2051647