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A classification of endo-commutative curled algebras of dimension 2 over a non-trivial field (2304.12510v1)
Published 25 Apr 2023 in math.RA
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.