On universal central extensions of Hom_Leibniz algebras

@article{Casas2012OnUC,
  title={On universal central extensions of Hom\_Leibniz algebras},
  author={Jos{\'e} Manuel Casas and Manuel A. Insua and N. Pacheco Rego},
  journal={arXiv: Rings and Algebras},
  year={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 study universal central extensions of Hom-Leibinz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of $\alpha$-central extension, universal $\alpha$-central extension and $\alpha$-perfect Hom-Leibniz algebra. We prove that an $\alpha$-perfect Hom… 
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References

SHOWING 1-9 OF 9 REFERENCES
On Universal Central Extensions of Leibniz Algebras
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)
(Co)Homology and universal central extension of Hom-Leibniz algebras
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)
On Hom-algebra structures
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
Hom-algebras and homology
Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as
Hom-algebras as deformations and homology
Universal enveloping algebras of Leibniz algebras and (co)homology
The homology of Lie algebras is closely related to the cyclic homology of associative algebras [LQ]. In [L] the first author constructed a "noncommutative" analog of Lie algebra homology which is,
Enveloping algebras of Hom-Lie algebras
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed. 2000 MSC: 05C05, 17A30, 17A32, 17A50, 17B01, 17B35, 17D25 1