Document Type : Original Article
Authors
1 Department of Mathematics, Faculty of Sciences, University of Sfax, Sfax, Tunisia
2 Department of Mathematics, Faculty of Sciences, University of Gafsa, Gafsa, Tunisia
3 IRIMAS-Department of Mathematics, Faculty of Sciences, University of Haute Alsace, Mulhouse, France
Abstract
In this paper, we study the structure and algebraic varieties of associative trialgebras. In partic-
ular, we classify all associative trialgebras of dimension at most four over a field of characteristic zero. Based on this classification, we provide a detailed analysis of their derivations and centroids. We also investigate the role of centroids in the structural theory of associative trialgebras and compute them explicitly for each isomorphism class in low dimensions. All computations are performed using symbolic computation software such as Mathematica. These results offer new insights into the algebraic and geometric aspects of associative
trialgebras.
Keywords
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