Dendrification of Hom-Malcev algebras

TL;DR

This paper introduces Hom-M-dendriform algebras, a new algebraic structure related to Hom-Malcev algebras, expanding the framework of Hom-algebraic structures and their interconnections.

Contribution

It defines Hom-M-dendriform algebras, explores their relation to Hom-pre-Malcev algebras, and connects them with Hom-alternative quadri-algebras, broadening the theory of Hom-algebras.

Findings

Hom-M-dendriform algebras are introduced as dendriform versions of Hom-Malcev algebras.

They are shown to relate to the $ ext{O}$-operator of Hom-pre-Malcev algebras.

Connections with Hom-alternative quadri-algebras are established.

Abstract

The main goal of this work is to introduce the notion of Hom-M-dendriform algebras which are the dendriform version of Hom-Malcev algebras. In fact they are the algebraic structures behind the $\mathcal{O}$-operator of Hom-pre-Malcev algebras. They also fit into a bigger framework as Hom-Malcev algebraic analogues of Hom-L-dendriform algebras. Furthermore, we show a connections between Hom-M-Dendriform algebras and Hom-alternative quadri-algebras.