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arXiv · 2501.10779

On the centre of crossed modules of Lie algebras

Mariam Pirashvili
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Abstract

This paper studies the relationship between crossed modules of Lie algebras and their centres. We show that any crossed module \(\partial : L_1\to L_0\) of Lie algebras fits in an exact sequence involving cohomology of the homotopy Lie algebras \(\pi_0(L_*)\) and \(\pi_1(L_*)\).

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Mariam Pirashvili. 2025-01-18. On the centre of crossed modules of Lie algebras. https://arxiv.org/abs/2501.10779

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