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Classification, α-Inner Derivations and α-Centroids of Finite-Dimensional Complex Hom-Trialgebras

This article focuses on the classification, α-inner-derivations and α-centroids of complex Hom-trialgebras up to dimension three. The initial research on these algebras was conducted by Loday and Ronco, and this paper builds upon their work by utilizing computer algebra software (Mathematica) to analyze the equations that define the structure constants. Furthermore, we explore the concept of α-inner-derivations and α-centroids of complex Hom-trialgebras. The findings reveal that for 2- and 3-dimensional algebras, there is only one trivial α-inner-derivation. However, there exist 23 non-isomorphic α-inner-derivations for 2- and 3-dimensional algebras. Regarding α-centroids, we identify trivial isomorphism classes for 2- and 3-dimensional Hom-trialgebras. Additionally, there are 11 non-isomorphic classes for 2-dimensional Hom-trialgebras and 19 for 3-dimensional algebras. The range of dimensions for both α-inner-derivations and α-centroids spans from 0 to 3.

Hom-Associative Trialgebra, Classification, α-Inner-derivation, α-Centroid

APA Style

Mosbahi, B., Zahari, A., Basdouri, I. (2023). Classification, α-Inner Derivations and α-Centroids of Finite-Dimensional Complex Hom-Trialgebras. Pure and Applied Mathematics Journal, 12(5), 86-97. https://doi.org/10.11648/j.pamj.20231205.12

ACS Style

Mosbahi, B.; Zahari, A.; Basdouri, I. Classification, α-Inner Derivations and α-Centroids of Finite-Dimensional Complex Hom-Trialgebras. Pure Appl. Math. J. 2023, 12(5), 86-97. doi: 10.11648/j.pamj.20231205.12

AMA Style

Mosbahi B, Zahari A, Basdouri I. Classification, α-Inner Derivations and α-Centroids of Finite-Dimensional Complex Hom-Trialgebras. Pure Appl Math J. 2023;12(5):86-97. doi: 10.11648/j.pamj.20231205.12

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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