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

2025/07/28 by Takahasi, Sin-Ei, Shirayanagi, Kiyoshi
#13A99 #FOS: Mathematics #Primary 17A30 #Rings and Algebras (math.RA) #Secondary 17D99

paper · doi:10.48550/arxiv.2507.20572

Abstract

A curled algebra is a non-associative algebra in which x and x² 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.

Citations

• Classification of three-dimensional anti-dendriform algebras
• A classification of endo-commutative curled algebras of dimension 2 over a non-trivial field

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