Kupershmidt operators on Hom-Malcev algebras and their deformation

Autor:	Harrathi, Fattoum, Mabrouk, Sami, Ncib, Othmen, Silvestrov, Sergei
Rok vydání:	2022
Předmět:	Mathematics - Rings and Algebras Mathematical Physics Mathematics - Quantum Algebra Mathematics - Representation Theory 17D30 17B61 17D10 17A01 17A30 17B10
Druh dokumentu:	Working Paper
DOI:	10.1142/S0219887823500469
Popis:	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. Comment: arXiv admin note: substantial text overlap with arXiv:2105.00606; text overlap with arXiv:1803.09287 by other authors
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.03762 Zobrazit plný text záznamu View this record from Arxiv