Research Article
Classification, α-Inner Derivations and α-Centroids of Finite-Dimensional Complex Hom-Trialgebras
Bouzid Mosbahi*,
Ahmed Zahari,
Imed Basdouri
Issue:
Volume 12, Issue 5, October 2023
Pages:
86-97
Received:
6 November 2023
Accepted:
5 December 2023
Published:
25 December 2023
Abstract: 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.
Abstract: 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 const...
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