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On the universal α-central extension of the semidirect product of Hom-Leibniz algebras
We introduce Hom-actions, semidirect product and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial properties
A Non-abelian Tensor Product of Hom–Lie Algebras
Non-abelian tensor product of Hom–Lie algebras is constructed and studied. This tensor product is used to describe universal ($$\alpha $$α)-central extensions of Hom–Lie algebras and to establish a
On universal central extensions of Hom-Lie algebras
We develop a theory of universal central extensions of Hom-Lie algebras. Classical results of universal central extensions of Lie algebras cannot be completely extended to Hom-Lie algebras setting,
On universal central extensions of Hom_Leibniz algebras
In the category of Hom-Leibniz algebras we introduce the notion of representation as adequate coefficients to construct the chain complex to compute the Leibniz homology of Hom-Leibniz algebras. We
Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras
In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in
Universal $\alpha$-central extensions of hom-Leibniz $n$-algebras
We construct homology with trivial coefficients of Hom-Leibniz $n$-algebras. We introduce and characterize universal ($\alpha$)-central extensions of Hom-Leibniz $n$-algebras. In particular, we show
On the Universal $$\alpha $$α-Central Extension of the Semi-direct Product of Hom-Leibniz Algebras
We introduce Hom-actions, semidirect product, and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial