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arXiv · 2402.18952

A classification of 2-dimensional endo-commutative straight algebras of type II_1

Sin-Ei Takahasi·Kiyoshi Shirayanagi·Makoto Tsukada
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Abstract

In this paper, we present a complete classification of 2-dimensional endo-commutative straight algebras of type II$_1$ over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves multiplication. A 2-dimensional straight algebra satisfies the condition that there exists an element $x$ such that $x$ and $x^2$ are linearly independent. The term type II$_1$ denotes a distinguishing characteristic of its structure matrix, which has rank 2. We provide multiplication tables for these algebras, listing them up to isomorphism.

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Sin-Ei Takahasi, Kiyoshi Shirayanagi, Makoto Tsukada. 2024-02-29. A classification of 2-dimensional endo-commutative straight algebras of type II_1. https://arxiv.org/abs/2402.18952

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