Cohomology of 3-dimensional color Lie algebras

Journal of Algebra. 2007. Vol. 316. No. 2. P. 499–513.

Пионтковский Д. И., Сильвестров С.

We develop the cohomology theory of color Lie superalgebras due to Scheunert--Zhang in a framework of nonhomogeneous quadratic Koszul algebras. In this approach, the Chevalley--Eilenberg complex of a color Lie algebra becomes a standard Koszul complex for its universal enveloping algebra. As an application, we calculate cohomologies with trivial coefficients of 3-dimensional color Lie superalgebras.