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Kiyoshi Shirayanagi

Publications and source records attributed to Kiyoshi Shirayanagi.

8 recordsLinked to original sources
arXiv2025

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

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.

math.RA↗
arXiv2024

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

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.

math.RA↗
arXiv2023

A Classification of 2-dimensional endo-commutative straight algebras of type I

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.

math.RA↗
arXiv2023

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 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.

math.RA↗
arXiv2023

A classification of endo-commutative curled algebras of dimension 2 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 endo-commutative curled algebras of dimension 2 over an arbitrary non-trivial field, where a curled algebra satisfies the condition that the square of any element is a scalar multiple of that element. We list all multiplication tables of the algebras up to isomorphism.

math.RA↗
arXiv2022

A Classification of Two-dimensional Endo-commutative Algebras over F_2

We introduce a new class of algebras called endo-commutative algebras in which the square mapping preserves multiplication, and provide a complete classification of endo-commutative algebras of dimension 2 over the field F_2 of two elements. We list all multiplication tables of the algebras up to isomorphism. This clarifies the difference between commutativity and endo-commutativity of algebras.

math.RA↗