Searcharxiv⌕ Search

arXiv subjects

N. Pacheco Rego

Publications and source records attributed to N. Pacheco Rego.

6 recordsLinked to original sources
arXiv2019

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 the Lie-center, call them Lie-central derivations. We provide a characterization of Lie-stem Leibniz algebras by their Lie-central derivations, and prove several properties of the Lie algebra of Lie-central derivations for Lie-nilpotent Leibniz algebras of class 2. We also introduce ${\sf ID}_*-Lie$-derivations. A ${\sf ID}_*-Lie$-derivation of a Leibniz algebra G is a Lie-derivation of G in which the image is contained in the second term of the lower Lie-central series of G, and that vanishes on Lie-central elements. We provide an upperbound for the dimension of the Lie algebra $ID_*^{Lie}(G)$ of $ID_*Lie$-derivation of G, and prove that the sets $ID_*^{Lie}(G)$ and $ID_*^{Lie}(G)$ are isomorphic for any two Lie-isoclinic Leibniz algebras G and Q.

math.RA↗
arXiv2016

Universal $α$-central extensions of hom-Leibniz $n$-algebras

We construct homology with trivial coefficients of Hom-Leibniz $n$-algebras. We introduce and characterize universal ($α$)-central extensions of Hom-Leibniz $n$-algebras. In particular, we show their interplay with the zeroth and first homology with trivial coefficients. When $n=2$ we recover the corresponding results on universal central extensions of Hom-Leibniz algebras. The notion of non-abelian tensor product of Hom-Leibniz $n$-algebras is introduced and we establish its relationship with the universal central extensions. We develop a generalization of the concept and properties of unicentral Leibniz algebras to the setting of Hom-Leibniz $n$-algebras.

math.RA↗
arXiv2016

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 ($α$-)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.

math.RA↗
arXiv2016

A non-abelian Hom-Leibniz tensor product and applications

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.

math.RA↗
arXiv2012

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 study universal central extensions of Hom-Leibinz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of $α$-central extension, universal $α$-central extension and $α$-perfect Hom-Leibniz algebra. We prove that an $α$-perfect Hom-Lie algebra admits a universal $α$-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both. In case $α= Id$ we recover the corresponding results on universal central extensions of Leibniz algebras.

math.RA↗