Cohomology of 3-dimensional color Lie algebras

We develop the cohomology theory of color Lie algebras due to Scheunert–Zhang in a framework of non-homogeneous 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, providing a constructive method for computation of cohomology. As an application, we compute cohomologies with trivial coefficients of -graded 3-dimensional color Lie algebras.