Geodesic
On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 249-264

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In this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras. Considering the Hom-Akivis superalgebra associated to a given Hom-Leibniz superalgebra, it is observed that the Hom-super Akivis identity leads to an additional property of Hom-Leibniz superalgebras, which in turn gives a necessary and sufficient condition for Hom-super Lie admissibility of Hom-Leibniz superalgebras. We also show that every (left) Hom-Leibniz superalgebra has a natural super Hom-Lie-Yamaguti structure.
Keywords: Hom-Leibniz superalgebras, Hom-Akivis superalgebras, Hom-Lie-Yamaguti superalgebras 
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Attan, Sylvain; Gaparayi, Donatien; Issa, A. Nourou. On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 249-264. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a3/