Classification, Derivations and Centroids of Low-Dimensional Real Trialgebras

TL;DR

This paper classifies low-dimensional associative trialgebras, explores their derivations and centroids, and provides detailed structural insights into these algebraic objects for dimensions up to four.

Contribution

It offers the first classification of n-dimensional associative trialgebras for n ≤ 4 and analyzes their derivations and centroids.

Findings

Classification of associative trialgebras for n ≤ 4

Explicit calculation of centroids for low-dimensional cases

Insights into the properties of centroids in associative trialgebras

Abstract

In this paper we study the structure and the algebraic varieties of associative trialgebras. We provide a classification of n-dimensional associative trialgebras for n $\leq$ 4. Using the classification result of associative trialgebras, we describe the derivations and centroids of low-dimensional associative trialgebras. We review some proprieties of the centroids in light of associative trialgebras and and we calculate the centroids of low-dimensional associative trialgebras.