Hochschild and cyclic homology of Yang–Mills algebras

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.