Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras

TL;DR

This paper explores the natural algebraic structures that can be derived from Hom-Malcev and Hom-alternative algebras, specifically establishing Hom-Lie triple systems and Hom-Bol algebra structures.

Contribution

It introduces the natural occurrence of Hom-Lie triple systems and Hom-Bol algebras within Hom-Malcev and Hom-alternative algebras, expanding their structural understanding.

Findings

Hom-Malcev algebras naturally form Hom-Lie triple systems.

Hom-Malcev and Hom-alternative algebras naturally admit Hom-Bol algebra structures.

These structures are compatible with the multiplicative property.

Abstract

Every multiplicative Hom-Malcev algebra has a natural multiplicative Hom-Lie triple system structure. Moreover, there is a natural Hom-Bol algebra structure on every multiplicative Hom-Malcev algebra and on every multiplicative right (or left) Hom-alternative algebra.