Cohomology of 3-dimensional color Lie algebras

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.