A characterization of endo-commutativity of 3-dimensional curled algebras

Fuente: arXiv
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Autores principales: Takahasi, Sin-Ei, Shirayanagi, Kiyoshi
Formato: Preprint
Publicado: 2025
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author Takahasi, Sin-Ei
Shirayanagi, Kiyoshi
author_facet Takahasi, Sin-Ei
Shirayanagi, Kiyoshi
contents A curled algebra is a non-associative algebra in which $x$ and $x^2$ are linearly dependent for every element $x$. An algebra is called endo-commutative, if the square mapping from the algebra to itself preserves multiplication. In this paper, we provide a necessary and sufficient condition for a 3-dimensional curled algebra over an arbitrary field to be endo-commutative, expressed in terms of the properties of its underlying linear basis.
format Preprint
id arxiv_https___arxiv_org_abs_2507_20572
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A characterization of endo-commutativity of 3-dimensional curled algebras
Takahasi, Sin-Ei
Shirayanagi, Kiyoshi
Rings and Algebras
Primary 17A30, Secondary 17D99, 13A99
A curled algebra is a non-associative algebra in which $x$ and $x^2$ are linearly dependent for every element $x$. An algebra is called endo-commutative, if the square mapping from the algebra to itself preserves multiplication. In this paper, we provide a necessary and sufficient condition for a 3-dimensional curled algebra over an arbitrary field to be endo-commutative, expressed in terms of the properties of its underlying linear basis.
title A characterization of endo-commutativity of 3-dimensional curled algebras
topic Rings and Algebras
Primary 17A30, Secondary 17D99, 13A99
url https://arxiv.org/abs/2507.20572