Hochschild and cyclic homology of Yang-Mills algebras

A. SOLOTAR; E. HERSCOVICH

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK

WALTER DE GRUYTER & CO

Lugar: Berlin; Año: 2012 vol. 665 p. 73 - 156

0075-4102

   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 [7], continuing thus the study of these algebras that we have initiated in [16]. The computation involves the use of a spectral sequence associated to the natural filtration on the universalenveloping 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.