Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras
Abdenacer Makhlouf, Sergei Silvestrov

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
