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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 (m,g,µ) and of the Lie algebra g/Im(µ). Moreover, a relationship between the ChevalleyEilenberg homology with coefficients and the homology of a crossed module of Lie algebras is established.

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