Journal of Lie Theory

no. 2
On the Centre of Crossed Modules of Lie Algebras
Journal of Lie Theory, Volume 35 (2025) no. 2, pp. 359-375

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 $\pi_1(L_*)$

Received:
Revised:
Accepted:
DOI: 10.5802/jolt.1387 
@article{JOLT_2025_35_2_a5,
     author = {M. Pirashvili},
     title = {On the {Centre} of {Crossed} {Modules} of {Lie} {Algebras
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     journal = {Journal of Lie Theory},
     pages = {359--375},
     year = {2025},
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     doi = {10.5802/jolt.1387},
     zbl = {08075076},
     language = {en},
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M. Pirashvili. On the Centre of Crossed Modules of Lie Algebras. Journal of Lie Theory, Volume 35 (2025) no. 2, pp. 359-375. doi: 10.5802/jolt.1387

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