Cohomology of Yang-Mills algebras.
Summary: 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 \(\mathfrak{so}(n)\ltimes\mathbb C^n\) acts by derivations upon \(U(YM)\). One of the important consequences of our results is that if \(n\geq 3\) then the Lie algebra of outer derivations of \(U(YM)\) coincides with \(\mathfrak{so}(n)\ltimes\mathbb C^n\).
scientific article; zbMATH DE number 5311249