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arXiv · 2205.03762

Kupershmidt operators on Hom-Malcev algebras and their deformation

Fattoum Harrathi·Sami Mabrouk·Othmen Ncib·Sergei Silvestrov
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Abstract

The main feature of Hom-algebras is that the identities defining the structures are twisted by linear maps. The purpose of this paper is to introduce and study a Hom-type generalization of pre-Malcev algebras, called Hom-pre-Malcev algebras. We also introduce the notion of Kupershmidt operators of Hom-Malcev and Hom-pre-Malcev algebras and show the connections between Hom-Malcev and Hom-pre-Malcev algebras using Kupershmidt operators. Hom-pre-Malcev algebras generalize Hom-pre-Lie algebras to the Hom-alternative setting and fit into a bigger framework with a close relationship with Hom-pre-alternative algebras. Finally, we establish a deformation theory of Kupershmidt operators on a Hom-Malcev algebra in consistence with the general principles of deformation theories and introduce the notion of Nijenhuis elements.

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Fattoum Harrathi, Sami Mabrouk, Othmen Ncib, Sergei Silvestrov. 2022-05-08. Kupershmidt operators on Hom-Malcev algebras and their deformation. https://doi.org/10.1142/s0219887823500469

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