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The basic objective of the current research paper is to investigate thestructure and the algebraic varieties of Hom-associative dialgebras. Weelaborate a classification of $n$-dimensional Hom-associative dialgebras for$n\leq4$. Additionally, using the classification result of Hom-associativedialgebras, we characterize the $\alpha$-derivations and centroids oflow-dimensional Hom-associative dialgebras. Furthermore, we equally tacklecertain features of derivations and centroids in the light of associativedialgebras and compute the centroids of low-dimensional associative dialgebras.

Classification, $\alpha^k$-Derivations and Centroids of $4$-dimensional Complex Hom-associative Dialgebras