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Cohomology of 3-dimensional color Lie algebras

Dmitri Piontkovski·Sergei Silvestrov
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Abstract

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.

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Dmitri Piontkovski, Sergei Silvestrov. 2005-08-29. Cohomology of 3-dimensional color Lie algebras. https://arxiv.org/abs/math/0508573

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