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 Z(2)(n)-graded 3-dimensional color Lie algebras. 2 (c) 2006 Elsevier Inc. All rights reserved.