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

• Main Authors: Mosbahi, Bouzid, Zahari, Ahmed, Basdouri, Imed
• Format: Journal Article
• Language: English
• Published: 30-04-2023
• Subjects: Mathematics - Rings and Algebras
• DOI: 10.48550/arxiv.2305.00471

In the current research work, our basic objective is to investigate the
stucture of Hom-associative trialgebras. Next, we build up one important class
of Hom-associative trialgebras and provide properties of right, left and meddle
operations in Hom-associative trialgebras. Furthermore, we describe the
classification of $n$-dimensional Hom-associative trialgebras for $n\leq 3$.
Additionally, the properties of the Inner-derivations and centroids are
identified and discussed. Eventually the Inner-derivations and centroids are
computed.