Homologies of cubic Artin-Schelter regular algebras
type: Item
instance of: scholarly article
title: Homologies of cubic Artin-Schelter regular algebras
zbMATH Open document ID: 1067.53064
author: Nicolas Marconnet
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: The author computes the Hochschild homology of Artin-Schelter regular algebras with global dimension 3 and cubic relations. Let us recall that the Hochschild homology of AS-regular algebras were already computed in the case of quadratic relations. Here, the author considers the case of cubic relations and generic coefficients. The main idea used is to see these algebras as deformations of a polynomial algebra equipped with a Poisson structure. Finally, the Hochschild cohomology is also studied and a Poincaré duality is obtained.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 16S37
Mathematics Subject Classification ID: 16S38
Mathematics Subject Classification ID: 17B63
zbMATH DE Number: 2105349
zbMATH Keywords: homologies
zbMATH Keywords: regular algebras
zbMATH Keywords: deformations
zbMATH Keywords: Poisson brackets
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.11.019
OpenAlex ID: W2075810953
cites work: Graded algebras of global dimension 3
cites work: Q3972720
cites work: Modules over regular algebras of dimension 3
cites work: Koszulity for nonquadratic algebras.
cites work: Homogeneous algebras.
cites work: Q3843687
cites work: A differential complex for Poisson manifolds
cites work: Yang-Mills algebra
cites work: Cyclic homology of enveloping algebras
cites work: Q3957087
cites work: Cyclic homology of universal enveloping algebras of Lie algebras of dimension 3
cites work: Noncommutative homology of some three-dimensional quantum spaces
cites work: Q4296949
DOI: 10.1016/J.JALGEBRA.2003.11.019
description: scientific article; zbMATH DE number 2105349