A classification of endo-commutative curled algebras of dimension 2 over a non-trivial field

2023/04/25 by Takahasi, Sin-Ei, Shirayanagi, Kiyoshi, Tsukada, Makoto · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2304.12510

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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