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arXiv · 2304.12510

A classification of endo-commutative curled algebras of dimension 2 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 endo-commutative curled algebras of dimension 2 over an arbitrary non-trivial field, where a curled algebra satisfies the condition that the square of any element is a scalar multiple of that element. We list all multiplication tables of the algebras up to isomorphism.

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Sin-Ei Takahasi, Kiyoshi Shirayanagi, Makoto Tsukada. 2023-04-25. A classification of endo-commutative curled algebras of dimension 2 over a non-trivial field. https://arxiv.org/abs/2304.12510

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