Cohomology of 3-dimensional color Lie algebras

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.

References in corpus (2)

• Bosonic realizations of the color analogue of the Heisenberg Lie algebra
• The second cohomology of sl(m|1) with coefficients in its enveloping algebra is trivial