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In the current research work, our basic objective is to investigate thestucture of Hom-associative trialgebras. Next, we build up one important classof Hom-associative trialgebras and provide properties of right, left and meddleoperations in Hom-associative trialgebras. Furthermore, we describe theclassification of $n$-dimensional Hom-associative trialgebras for $n\leq 3$.Additionally, the properties of the Inner-derivations and centroids areidentified and discussed. Eventually the Inner-derivations and centroids arecomputed.

Classification, $\alpha$-Inner Derivations and $\alpha$-Centroids of Finite-Dimensional Complex Hom-Trialgebras