Cohomology of Yang–Mills algebras

Abstract

In this paper 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 so(n) ⋉ ℂn acts by derivations upon U(YM). One of the important consequences of our results is that if n ≥ 3 then the Lie algebra of outer derivations of U(YM) coincides with so(n) ⋉ ℂn.