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Classification of ($\rho,\tau,\sigma$)-derivations of two-dimensional left-symmetric dialgebras

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arxiv 2411.05716 v1 pith:ESVOOECC submitted 2024-11-08 math.RA

Basdouri Imed , Bouzid Mosbahi This is my paper · ORCID
classification math.RA
keywords derivationsclassificationdialgebrasgeneralizedleft-symmetrictwo-dimensionaladditionallyadmissible
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abstract

We introduce and study a generalized form of derivations for dendriform algebras, specifying all admissible parameter values that define these derivations. Additionally, we present a complete classification of generalized derivations for two-dimensional left-symmetric dialgebras over the field $\mathbb{K}$.

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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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