Journal of Lie Theory 35 (2025), No. 2, 359--375
Copyright Heldermann Verlag 2025
On the Centre of Crossed Modules of Lie Algebras
Mariam Pirashvili
Dept. Mathematical Sciences, University of Plymouth, United Kingdom
mariam.pirashvili@plymouth.ac.uk
[Abstract-pdf]
This paper studies the relationship between crossed modules of Lie algebras and their centres. We show that the homotopy of the centre of 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 \(\pi_1(L_*)\).
Keywords: Crossed modules, Lie algebra cohomology, Drinfeld centre.
MSC: 18G45, 17B55.
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