Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

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

Pages: 185 – 194

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a12

Authors

Guram Donadze (Kerala School of Mathematics, Kerala, India)

Manuel Ladra (Department of Algebra, University of Santiago de Compostela, Spain)

Abstract

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

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