On Universal Central Extensions of Leibniz Algebras |
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| Authors: | J M Casas N Corral |
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| Affiliation: | 1. Department of Applied Mathematics I , University of Vigo, E. U. I. T. Forestal , Pontevedra , Spain jmcasas@uvigo.es;3. Department of Mathematics, Statistics and Computers Science, Faculty of Science , University of Cantabria , Santander , Spain |
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| Abstract: | We construct the endofunctor 𝔲𝔠𝔢 between the category of Leibniz algebras which assigns to a perfect Leibniz algebra its universal central extension, and we obtain the isomorphism 𝔲𝔠𝔢Lie(𝔮Lie) ? (𝔲𝔠𝔢Leib(𝔮))Lie, where 𝔮 is a perfect Leibniz algebra satisfying the condition x, x, y]] + x, y], x] = 0, for all x, y ∈ 𝔮. Moreover, we obtain several results concerning the lifting of automorphisms and derivations in a covering. We also study the relationship between the universal central extension of a semidirect product of perfect Leibniz algebras and the semidirect product of the universal central extension of both of them. |
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| Keywords: | Leibniz algebra Leibniz homology Universal central extension |
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