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arXiv · 2507.20572

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

Sin-Ei Takahasi·Kiyoshi Shirayanagi
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Abstract

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.

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Sin-Ei Takahasi, Kiyoshi Shirayanagi. 2025-07-28. A characterization of endo-commutativity of 3-dimensional curled algebras. https://arxiv.org/abs/2507.20572

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