On Lie-central extensions of Leibniz algebras

2015/04/10 by Casas, J. M., Khmaladze, E. · 2 citations
#17A32 #17B55 #18D99 #18G35 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1504.02639

Abstract

Basing ourselves on the categorical notions of central extensions and commutators in the framework of semi-abelian categories relative to a Birkhoff subcategory, we study central extensions of Leibniz algebras with respect to the Birkhoff subcategory of Lie algebras, called Lie-central extensions. We obtain a six-term exact homology sequence associated to a Lie-central extension. This sequence, together with the relative commutators, allows us to characterize several classes of Lie-central extensions, such as Lie-trivial, Lie-stem and Lie-stem cover, to introduce and characterize Lie-unicentral, Lie-capable, Lie-solvable and Lie-nilpotent Leibniz algebras.

Cited by

• On Lie-holomorphs of Leibniz algebras
• A characterization of perfect Leibniz algebras

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