A Classification of 2-dimensional endo-commutative straight algebras of type I
Sin-Ei Takahasi, Kiyoshi Shirayanagi, Makoto Tsukada
TL;DR
This paper classifies all 2-dimensional endo-commutative straight algebras of type I over any field, providing a comprehensive list of their multiplication tables up to isomorphism.
Contribution
It offers a complete classification and explicit listing of 2D endo-commutative straight algebras of type I, a previously uncharacterized class.
Findings
All such algebras are classified up to isomorphism.
Explicit multiplication tables are provided for each algebra.
The classification holds over any field.
Abstract
In this paper, we provide a complete classification of 2-dimensional endo-commutative straight algebras of type I over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves multiplication. Type I denotes a distinguishing characteristic of its structure matrix of rank 2. We list all multiplication tables of these algebras up to isomorphism.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Algebraic structures and combinatorial models