A classification of 2-dimensional endo-commutative straight algebras of rank 1 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 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-05
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
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2 satisfies the condition that there exists an element \(x\) such that \(x\) and \(x^2\) are linearly independent. We list all multiplication tables of the algebras up to isomorphism.
ISSN:2331-8422