Classification, Derivations and Centroids of Low-Dimensional Complex BiHom-Trialgebras

TL;DR

This paper explores the structure and classification of low-dimensional BiHom-trialgebras, focusing on their derivations, centroids, and properties of their operations, providing new insights into their algebraic characteristics.

Contribution

It introduces a classification of low-dimensional BiHom-trialgebras and characterizes their derivations and centroids, advancing understanding of their algebraic structure.

Findings

Classified n-dimensional BiHom-trialgebras for n ≤ 3

Characterized derivations and centroids of low-dimensional BiHom-trialgebras

Reviewed properties of centroids in BiHom-associative trialgebras

Abstract

The basic objective of this research work is to investigate the stucture of BiHom-associative trialgebras.\,In this respect we build up one important class of BiHom-trialgebras and determine properties of right, left and middle operations in BiHom-associative trialgebras.\,We provide a classification of $n$-dimensional BiHom-trialgebras for $n\leq3$.\,Relying upon the classification result of BiHom-associative trialgebras, the derivations and centroids of low-dimensional BiHom-associative trialgebras are characterized.\,Certain properties of the centroids in light of BiHom-associative trialgebras are reviwed the centroids of low-dimensional BiHom-associative trialgebras are computed.