Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras
Anja Arfa, Nejib Saadaoui, Sergei Silvestrov
TL;DR
This paper reviews recent developments in Hom-Leibniz algebras, introduces symmetric Hom-Leibniz superalgebras, and classifies 2-dimensional cases, analyzing their centroids and derivations.
Contribution
It provides a classification of 2-dimensional Hom-Leibniz algebras and explores their centroids and derivations, including the introduction of symmetric Hom-Leibniz superalgebras.
Findings
Classification of 2-dimensional Hom-Leibniz algebras completed
Properties of symmetric Hom-Leibniz superalgebras established
Centroids and derivations of these algebras analyzed
Abstract
Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimensional Hom-Leibniz algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra