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Compatible Associative Algebras and Some Invariants

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arxiv 2405.18243 v2 pith:67BGAB4Y submitted 2024-05-28 math.RA

Erik Mainellis , Bouzid Mosbahi , Ahmed Zahari This is my paper · ORCID
classification math.RA
keywords associativealgebrascompatibleinvariantssomealgebraarticleautomorphisms
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A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as well as the classifications of their corresponding derivations, centroids, automorphisms, and quasi-centroids. We then characterize a selection of further invariants such as Rota-Baxter operators and second cohomology for some specific examples.

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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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