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arXiv · 2305.10629

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

Sin-Ei Takahasi·Kiyoshi Shirayanagi·Makoto Tsukada
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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 $x^2$ are linearly independent. We list all multiplication tables of the algebras up to isomorphism.

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Sin-Ei Takahasi, Kiyoshi Shirayanagi, Makoto Tsukada. 2023-05-18. A classification of 2-dimensional endo-commutative straight algebras of rank 1 over a non-trivial field. https://arxiv.org/abs/2305.10629

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