Chevalley-Eilenberg homology of crossed modules of Lie algebras in lower dimensions

In this paper we prove a five term exact sequence connecting in lower dimensions the Chevalley-Eilenberg homologies of the crossed module of Lie algebras $(\mathfrak{m}, \mathfrak{g}, \mu)$ and of the Lie algebra $\mathfrak{g}/ \mathrm{Im} (\mu)$. Moreover, a relationship between the Chevalley-Eilenberg homology with coefficients and the homology of a crossed module of Lie algebras is established.

Keywords

crossed modules of Lie algebras, Chevalley-Eilenberg homology

2010 Mathematics Subject Classification

17B40, 17B56, 18G50, 18G60, 19D55

Full Text (PDF format)

Published 4 December 2014