Hochschild cohomology and stratifying ideals.
type: Item
instance of: scholarly article
title: Hochschild cohomology and stratifying ideals.
zbMATH Open document ID: 1181.16009
author: Steffen Koenig
author: Hiroshi Nagase
published in: Journal of Pure and Applied Algebra
publication date: 2009-03-10T00:00:00Z
review text: Given an algebra \(B\) and a stratifying ideal \(I=BeB\) of \(B\), where \(e\) is an idempotent generating \(I\), the authors establish a long exact sequence relating the Hochschild cohomology groups of the algebras \(B\), \(B/I\) and \(eBe\). This generalizes many results in the literature. The authors also study the quotient of the Hochschild cohomology algebra modulo the ideal generated by all homogeneous nilpotent elements. The authors show that such quotient for \(B\) embeds (as a graded algebra) into the product of the corresponding quotients for \(B/I\) and \(eBe\). Using this it is proved that such quotient is finitely generated in the case of the Brauer algebra \(B_k(3,\delta)\), verifying in this case a conjecture of Snashall and Solberg. Finally, the authors consider a condition under which the mentioned quotients for the algebras \(B\) and \(eBe\) are isomorphic.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16G30
zbMATH DE Number: 5527507
zbMATH Keywords: Hochschild cohomology groups
zbMATH Keywords: stratifying ideals
zbMATH Keywords: exact sequences
zbMATH Keywords: Hochschild cohomology algebras
zbMATH Keywords: Brauer algebras
MaRDI profile type: Publication
full work available at URL: j.jpaa.2008.10.012
OpenAlex ID: W2011845250
cites work: Q3240881
cites work: Q4405972
cites work: Stratifying endomorphism algebras
cites work: The Hochschild cohomology ring of a selfinjective algebra of finite representation type
cites work: THE HOCHSCHILD COHOMOLOGY RING MODULO NILPOTENCE OF A MONOMIAL ALGEBRA
cites work: Q3377705
cites work: Q4206909
cites work: Hochschild cohomology rings of algebras \(k[X]/(f)\)
cites work: A characteristic free approach to Brauer algebras
cites work: Hochschild cohomology of triangular matrix algebras
cites work: Hochschild cohomology of algebras with homological ideals.
cites work: Support varieties and Hochschild cohomology rings
DOI: 10.1016/J.JPAA.2008.10.012
description: scientific article; zbMATH DE number 5527507