Hom-left-symmetric color dialgebras, Hom-tridendriform color algebras and Yau's twisting generalizations

TL;DR

This paper introduces Hom-left-symmetric color dialgebras and Hom-tridendriform color algebras, explores their properties and connections with other Hom-color algebras, and generalizes Yau's twisting to produce new color Hom-algebras.

Contribution

It presents new classes of Hom-color algebras, studies their properties and relationships, and extends Yau's twisting method to a broader class of color Hom-algebras.

Findings

Established properties of Hom-left-symmetric color dialgebras.

Connected Hom-tridendriform color algebras with other Hom-color structures.

Generalized Yau's twisting to produce new color Hom-algebras.

Abstract

The goal of this paper is to introduce and give some constructions and study properties of Hom-left-symmetric color dialgebras and Hom-tridendriform color algebras. Next, we study their connection with Hom-associative color algebra, Hom-post-Lie color algebra and Hom-Poisson color dialgebras. Finally, we generalize Yau's twisting to a class of color Hom-algebras and used endomorphisms or elements of centroids to produce other color Hom-algebras from given one.