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

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 t...

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Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Sin-Ei Takahasi, Shirayanagi, Kiyoshi, Tsukada, Makoto
Format: Article
Language:English
Subjects:
Algebra
Classification
Isomorphism
Mathematical tables
Multiplication
Online Access:Get full text
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Summary: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.
ISSN:2331-8422