A note on relations between Hom-Malcev algebras and Hom-Lie-Yamaguti algebras

TL;DR

This paper explores the relationship between Hom-Malcev algebras and Hom-Lie-Yamaguti algebras, showing that certain structures in one correspond to those in the other, especially over fields of characteristic zero.

Contribution

It establishes that a specific class of Hom-Lie-Yamaguti algebras can be characterized as multiplicative Hom-Malcev algebras and vice versa.

Findings

Hom-Lie-Yamaguti algebra with ternary operation expressed through binary operation is a multiplicative Hom-Malcev algebra.

Any multiplicative Hom-Malcev algebra over a field of characteristic zero admits a Hom-Lie-Yamaguti structure.

Abstract

A Hom-Lie-Yamaguti algebra, whose ternary operation expresses through its binary one in a specific way, is a multiplicative Hom-Malcev algebra. Any multiplicative Hom-Malcev algebra over a field of characteristic zero has a natural Hom-Lie-Yamaguti structure.