Cohomology of Yang–Mills algebras

  • Michael Movshev

    SUNY at Stony Brook


In this paper we compute cyclic and Hochschild homology of the universal envelope of the Yang–Mills Lie algebra . We also compute Hochschild cohomology with coefficients in , considered as a bimodule over itself.

The result of the calculations depends on the number of generators of . The semidirect product acts by derivations upon . One of the important consequences of our results is that if then the Lie algebra of outer derivations of coincides with .

Cite this article

Michael Movshev, Cohomology of Yang–Mills algebras. J. Noncommut. Geom. 2 (2008), no. 3, pp. 353–404

DOI 10.4171/JNCG/24