A Classification of 2-dimensional endo-commutative straight algebras of type I

2023/07/04 by Sin‐Ei Takahasi, Takahasi, Sin-Ei, Kiyoshi Shirayanagi +3
Mathematics · #13A99 (Secondary) #17A30 (Primary) 17D99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2307.01478

openalex publication_date 2023/07/04 · openalex created_date 2023/07/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide a complete classification of 2-dimensional endo-commutative straight algebras of type I over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves multiplication. Type I denotes a distinguishing characteristic of its structure matrix of rank 2. We list all multiplication tables of these algebras up to isomorphism.

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