Finite dimensional algebras with vanishing Hochschild cohomology
type: Item
instance of: scholarly article
title: Finite dimensional algebras with vanishing Hochschild cohomology
zbMATH Open document ID: 0926.16008
author: S. Gastaminza
author: José A. de la Peña
author: M. I. Platzeck
author: María Julia Redondo
author: Sonia Trepode
published in: Journal of Algebra
publication date: 1999-09-30T00:00:00Z
review text: Let \(Q\) be a finite quiver and \(A=kQ/I\) the basic algebra for an admissible ideal \(I\) and algebraically closed field \(k\). The authors analyze connections between vanishing of the higher Hochschild cohomologies \(H^i(A)\) and some properties of the quiver \(Q\). For instance, \(Q\) has no oriented cycles provided that the cohomology group \(H^1(A)\) strongly vanishes. Some features of the Auslander-Reiten quiver of an algebra are studied as well.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16G70
zbMATH DE Number: 1271641
zbMATH Keywords: admissible ideals
zbMATH Keywords: basic algebras
zbMATH Keywords: Hochschild cohomology
zbMATH Keywords: finite quivers
zbMATH Keywords: cohomology groups
zbMATH Keywords: Auslander-Reiten quivers
reviewed by: Marek Golasiński
MaRDI profile type: Publication
OpenAlex ID: W2090835384
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DOI: 10.1006/JABR.1998.7614
description: scientific article; zbMATH DE number 1271641