Cohomology of Yang–Mills algebras

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 inU.YM/, considered as a bimodule over itself. The result of the calculations depends on the number of generatorsn ofYM. The semidirect product so.n/ E C n acts by derivations uponU.YM/. One of the important consequences of our results is that ifn 3 then the Lie algebra of outer derivations ofU.YM/ coincides with so.n/ E C n .