• Corpus ID: 51962485

# On the universal α-central extension of the semidirect product of Hom-Leibniz algebras

@inproceedings{Casas2014OnTU,
title={On the universal $\alpha$-central extension of the semidirect product of Hom-Leibniz algebras},
author={Jos{\'e} Manuel Casas and N. Pacheco Rego},
year={2014}
}
• Published 2014
• Mathematics
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 of the universal (α)central extensions of (α)-perfect Hom-Leibniz algebras. We establish under what conditions an automorphism or a derivation can be lifted in an α-cover and we analyze the universal α-central extension of the semi-direct product of two αperfect Hom-Leibniz algebras.
2 Citations
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In this paper, we introduce a non-abelian exterior product of Hom-Leibniz algebras and investigate its relative to the Hopf’s formula. We also construct an eight-term exact sequence in the homology

## References

SHOWING 1-10 OF 23 REFERENCES
On Universal Central Extensions of Leibniz Algebras
• Mathematics
• 2009
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)
On universal central extensions of Hom_Leibniz algebras
• Mathematics
• 2012
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
(Co)Homology and universal central extension of Hom-Leibniz algebras
• Mathematics
• 2011
Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory (such as (co)homology groups, universal central extensions)
Some characterizations of Hom-Leibniz algebras
Some basic properties of Hom-Leibniz algebras are found. These properties are the Hom-analogue of corresponding well-known properties of Leibniz algebras. Considering the Hom-Akivis algebra
Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
• Mathematics
• 2010
Abstract The aim of this paper is to extend to Hom-algebra structures the theory of 1-parameter formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and
On Hom-algebra structures
• Mathematics
• 2006
A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov and
Monoidal Hom–Hopf Algebras
• Mathematics
• 2009
Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in
HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS
The main feature of Hom-algebras is that the identities deflning the structures are twisted by homomorphisms. The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan