A classification of 2-dimensional endo-commutative straight algebras of rank 1 over a non-trivial field

2023/05/18 by Sin‐Ei Takahasi, Takahasi, Sin-Ei, Kiyoshi Shirayanagi +3
Mathematics · #13A99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 17A30 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 17D99

paper · pdf · doi:10.48550/arxiv.2305.10629

openalex publication_date 2023/05/18 · openalex created_date 2023/05/21 · openalex updated_date 2026/07/28

Abstract

An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2 satisfies the condition that there exists an element x such that x and x² are linearly independent. We list all multiplication tables of the algebras up to isomorphism.

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