English

Hom-pre-Malcev and Hom-M-Dendriform algebras

Rings and Algebras 2021-11-09 v2

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 O\mathcal{O}-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 O\mathcal{O}-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}
}