Accessible Requires Authentication Published by De Gruyter June 28, 2011

Hochschild and cyclic homology of Yang–Mills algebras

Estanislao Herscovich and Andrea Solotar

Abstract

The aim of this article is to present a detailed algebraic computation of the Hochschild and cyclic homology groups of the Yang–Mills algebras YM(n) (n ∈ ℕ≧2) defined by A. Connes and M. Dubois-Violette in [8], continuing thus the study of these algebras that we have initiated in [17]. The computation involves the use of a spectral sequence associated to the natural filtration on the universal enveloping algebra YM(n) provided by a Lie ideal 𝔱𝔶𝔪(n) in 𝔶𝔪(n) which is free as Lie algebra. As a corollary, we describe the Lie structure of the first Hochschild cohomology group.

Received: 2009-07-27
Revised: 2010-09-28
Published Online: 2011-06-28
Published in Print: 2012-04

©[2012] by Walter de Gruyter Berlin Boston