Splitting of operations for Hom-diassociative and Hom-triassociative Algebras

TL;DR

This paper introduces Hom-quadri dendriform and Hom-six-dendriform algebras as splittings of Hom-diassociative and Hom-triassociative algebras, exploring their relationships and classifying low-dimensional cases.

Contribution

It presents new structures of Hom-algebras, establishing their connections and providing a classification in low dimensions.

Findings

Introduction of Hom-quadri dendriform and Hom-six-dendriform algebras

Analysis of relationships between these categories

Classification of Hom-quadri-dendriform algebra in low dimensions

Abstract

Hom-quadri dendriform algebras and Hom-six-dendriform agebras are introduced and studied which is a splitting of a Hom-diassociative and Hom-triassociative algebras, respectively. Moreover we explore the connections be tween these categories of Hom-algebras. Finally We elaborate a classification of Hom-quadri-dendriform algebra in low dimensional.