Classification, Derivations and Centroids of Low-Dimensional Real Trialgebras
Ahmed Zahari, Bouzid Mosbahi, Imed Basdouri

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 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.
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Taxonomy
TopicsAdvanced Topics in Algebra
