Cohomology of Yang-Mills algebras.
type: Item
instance of: scholarly article
title: Cohomology of Yang-Mills algebras.
zbMATH Open document ID: 1231.16007
DOI: 10.4171/JNCG/24
author: Michael Movshev
published in: Journal of Noncommutative Geometry
publication date: 2008-08-13T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: Summary: We compute cyclic and Hochschild homology of the universal envelope \(U(YM)\) of the Yang-Mills Lie algebra \(YM\). We also compute Hochschild cohomology with coefficients in \(U(YM)\), considered as a bimodule over itself. The result of the calculations depends on the number of generators \(n\) of \(YM\). The semidirect product \(\mathfrak{so}(n)\ltimes\mathbb C^n\) acts by derivations upon \(U(YM)\). One of the important consequences of our results is that if \(n\geq 3\) then the Lie algebra of outer derivations of \(U(YM)\) coincides with \(\mathfrak{so}(n)\ltimes\mathbb C^n\).
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 5311249
zbMATH Keywords: Yang-Mills algebras
zbMATH Keywords: cyclic cohomology
zbMATH Keywords: Hochschild homology
zbMATH Keywords: derivations
zbMATH Keywords: Yang-Mills Lie algebras
zbMATH Keywords: universal enveloping algebras
MaRDI profile type: Publication
cites work: Graded algebras of global dimension 3
cites work: Q4935949
cites work: Q4941498
cites work: Yang-Mills algebra
cites work: Q3633679
cites work: Q4783713
cites work: Cohomology of Lie algebras
cites work: Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)
OpenAlex ID: W2027129404
description: scientific article; zbMATH DE number 5311249