# 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…

## 11 Citations

Universal $\alpha$-central extensions of hom-Leibniz $n$-algebras

- Mathematics
- 2016

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

- Mathematics
- 2013

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…

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

- Mathematics
- 2014

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…

On universal $\alpha$-central extensions of Hom-preLie algebras

- Mathematics
- 2018

We introduce the notion of Hom-co-represention and low-dimensional chain complex. We study universal central extensions of Hom-preLie algebras and generlize some classical results. As the same time,…

ON THE UNIVERSAL α -CENTRAL EXTENSIONS OF THE SEMI-DIRECT PRODUCT OF HOM-PRELIE ALGEBRAS

- Mathematics
- 2020

. We study Hom-actions, semidirect product and describe the re-lation between semi-direct product extensions and split extensions of Hom- preLie algebras. We obtain the functorial properties of the…

A non-abelian exterior product of Hom-Leibniz algebras

- Mathematics
- 2021

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…

Universal central extensions of Hom-Lie antialgebras

- Mathematics
- 2019

We develop a theory of universal central extensions for Hom-Lie antialgebra. It is proved that a Hom-Lie antialgebra admits a universal central extension if and only if it is perfect. Moreover, we…

Applications of β-Nijenhuis-Richardson bracket to cohomology of Hom-algebras

- Mathematics
- 2021

In this paper, we mean by Hom-algebras a triple (M,d, β) in which M is a vector space, d a bilinear map on M and β : M → M (the twisting map). In this work we define the left, right and Lie…

1 1 O ct 2 01 2 A RELATIVE THEORY OF UNIVERSAL CENTRAL EXTENSIONS

- Mathematics
- 2021

Basing ourselves on Janelidze and Kelly’s general notion of central extension, we study universal central extensions in the context of semi-abelian categories. Thus we unify classical, recent and new…

Multipliers and Covers of Perfect Diassociative Algebras

- Mathematics
- 2022

The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with…

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