Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras

TL;DR

This paper generalizes Lie-admissible coalgebras to Hom-coalgebras and introduces Hom-Hopf algebras, expanding the framework of Hom-algebra structures with new properties and potential applications.

Contribution

It extends Lie-admissible coalgebras to the Hom setting and introduces Hom-Hopf algebras, providing new structures and properties in Hom-algebra theory.

Findings

Definition of Hom-Lie admissible Hom-coalgebras

Introduction of Hom-Hopf algebras with specific properties

Extension of Hom-algebra structures to coalgebra context

Abstract

The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced by Goze and Remm to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced by the authors.