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.
Cite this article
Michael Movshev, Cohomology of Yang–Mills algebras. J. Noncommut. Geom. 2 (2008), no. 3, pp. 353–404DOI 10.4171/JNCG/24