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Classification of Low-dimensional Complex Triassociative Algebras

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arxiv 2209.04351 v1 pith:PNTEYA2Z submitted 2022-09-09 math.RA

Erik Mainellis This is my paper · ORCID
classification math.RA
keywords algebrastriassociativeassociativeclassificationcomplexdimensionallodaycharacterized
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The paper concerns associative trialgebras, also known as triassociative algebras, which were first studied by Loday and Ronco in 2001. These generalize Loday's associative dialgebras (diassociative algebras) and are characterized by 3 operations and 11 identities. The paper details the classification of 1-dimensional and 2-dimensional triassociative algebras over a complex vector space.

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Cited by 1 Pith paper

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  1. Crossed modules of ternary Leibniz algebras

    math.RA 2025-01 reject novelty 4.0 of 10

    The paper transfers crossed modules from triassociative and Leibniz algebras to ternary Leibniz algebras, but omits the supporting computations and contains garbled formulas.

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