Schur- and Baer-type theorems for Lie and Leibniz algebras

Donadze, Guram;Van der Linden, Tim
(2023) Belgian Mathematical Society - Simon Stevin. Bulletin — Vol. 30, n° 3, p. 386-398 (2023)

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  • Donadze, GuramInstitute of Cybernetics of Georgian Tech Univ
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  • Van der Linden, Timorcid-logoUCLouvain
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Abstract
The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products and exterior products, we prove Schur's Theorem for finitely generated Leibniz algebras, both Schur's Theorem and Baer's Theorem for finitely generated Lie algebras, and a version of these theorems for finitely presented Lie algebras.
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Donadze, G., & Van der Linden, T. (2023). Schur- and Baer-type theorems for Lie and Leibniz algebras. Belgian Mathematical Society - Simon Stevin. Bulletin, 30(3), 386-398. https://doi.org/10.36045/j.bbms.230609 (Original work published 2023)