Variety of Hom-Sabinin algebras and related algebra subclasses

TL;DR

This paper explores Hom-type Sabinin algebras, establishing their connections with Lie, Malcev, Bol, and other algebra classes, and introduces a new Hom-bialgebra concept linked to universal enveloping algebras.

Contribution

It provides a general construction linking identities of Hom-algebras with classical algebras and introduces the concept of Hom-bialgebras and their primitive elements.

Findings

Hom-type Lie, Malcev, Bol algebras are Sabinin algebras of Hom-type

A key construction relates identities of Hom-algebras to classical algebras

Introduction of Hom-bialgebra and primitive element study

Abstract

The purpose of this paper is to study Sabinin algebras of Hom-type. It is shown that Lie, Malcev, Bol and other algebras of Hom-type are naturally Sabinin algebras of Hom-type. To this end, we provide a general key construction that establish a relationship between identities of some class of Hom-algebras and ordinary algebras. Moreover, we discuss a new concept of Hom-bialgebra, in relation with universal enveloping Hom-algebras. A study based on primitive elements is provided.