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Classification, Derivations and Centroids of Low-Dimensional Complex BiHom-Trialgebras

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arxiv 2304.06781 v1 pith:PUT57ZVY submitted 2023-04-13 math.RA

Ahmed Zahari , Bouzid Mosbahi , Imed Basdouri This is my paper · ORCID
classification math.RA
keywords bihom-associativetrialgebrascentroidsbihom-trialgebrasclassificationlow-dimensionalderivationsproperties
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abstract

The basic objective of this research work is to investigate the stucture of BiHom-associative trialgebras.\,In this respect we build up one important class of BiHom-trialgebras and determine properties of right, left and middle operations in BiHom-associative trialgebras.\,We provide a classification of $n$-dimensional BiHom-trialgebras for $n\leq3$.\,Relying upon the classification result of BiHom-associative trialgebras, the derivations and centroids of low-dimensional BiHom-associative trialgebras are characterized.\,Certain properties of the centroids in light of BiHom-associative trialgebras are reviwed the centroids of low-dimensional BiHom-associative trialgebras are computed.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Computational Approaches to Derivations and Automorphism Groups of Associative Algebras

    math.RA 2025-01 reject novelty 4.0 of 10

    The paper claims to compute derivations and automorphism groups of low-dimensional associative algebras over C, but the computations are not self-contained and contain errors.

  2. Rota-type operators on 2-dimensional dendriform algebras

    math.RA 2024-11 reject novelty 4.0 of 10

    The claimed classifications of Rota-type operators on 2D dendriform algebras are invalid as stated, with table entries that fail the defining operator equations.

  3. Central derivations of low-dimensional Zinbiel algebras

    math.RA 2024-11 reject novelty 3.0 of 10

    The tabulated central derivations for low-dimensional Zinbiel algebras contain entries that violate the paper's own definition, so the classification is unreliable.

  4. An Algorithmic Approach to Inner Derivations of Low-Dimensional Zinbiel Algebras

    math.RA 2024-12 reject novelty 2.0 of 10

    The central claim that ad_w(u)=u∘w-w∘u is a derivation of every Zinbiel algebra is false; a counterexample appears in the paper's own four-dimensional table.

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