Structures and comodules of Hom-post Lie coalgebras

TL;DR

This paper introduces dual notions of Hom-tridendriform and Hom-post-Lie coalgebras, explores their properties and relationships, and constructs comodules via twisting methods, advancing the understanding of Hom-coalgebra structures.

Contribution

It defines Hom-tridendriform and Hom-post-Lie coalgebras, studies their properties and connections, and develops methods to construct comodules through twisting techniques.

Findings

Defined Hom-tridendriform and Hom-post-Lie coalgebras.

Established properties and relationships among these coalgebras.

Constructed comodules using Yau twisting methods.

Abstract

In this paper, we introduce the notions of Hom-tridendriform coalgebras and Hom-post-Lie coalgebras as the dual notions of Hom-tridendriform algebras and Hom-post-LIe algebras respectively. We give some properties related to them. Then, we study the relationships between them and their connection with post-Hom-Poisson coalgebras. Next, using the Yau stwisting in the modules case, we give some constructions of comodules over post-Hom-Lie coalgebras by twisting either the comodule structures or post-Hom-Lie coalgebra structures.