Hom-pre-Malcev and Hom-M-Dendriform algebras
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 and M-dendriform algebras, called Hom-pre-Malcev algebras and Hom-M-dendriform algebras. We also introduce the notion of -operators of Hom-Malcev and Hom-pre-Malcev algebras and show the connections between Hom-Malcev, Hom-pre-Malcev and Hom-M-dendriform algebras using -operators. Hom-pre-Malcev algebras and Hom-M-dendriform algebras generalize Hom-pre-Lie algebras and Hom-L-dendriform algebras respectively to the alternative setting and fit into a bigger framework with a close relationship with Hom-pre-alternative algebras and Hom-alternative quadri-algebras respectively.
Keywords
Cite
@article{arxiv.2105.00606,
title = {Hom-pre-Malcev and Hom-M-Dendriform algebras},
author = {Fattoum Harrathi and Sami Mabrouk and Othmen Ncib and Sergei Silvestrov},
journal= {arXiv preprint arXiv:2105.00606},
year = {2021}
}