arXiv subjects
Publications and source records attributed to E. Khmaladze.
We study some properties of the non-abelian tensor product of Hom-Lie algebras concerning the preservation of products and quotients, solvability and nilpotency, and describe compatibility with the universal central extensions of perfect Hom-Lie algebras.
Non-abelian tensor product of Hom-Lie algebras is constructed and studied. This tensor product is used to describe universal ($α$-)central extensions of Hom-Lie algebras and to establish a relation between cyclic and Milnor cyclic homologies of Hom-associative algebras satisfying certain additional condition.
The notion of non-abelian Hom-Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the universal ($α$-)central extensions of Hom-Leibniz algebras. We also give its application to the Hochschild homology of Hom-associative algebras.
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.