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Makoto Tsukada

Publications and source records attributed to Makoto Tsukada.

7 recordsLinked to original sources
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↗
arXiv2004

Law of Error in Tsallis Statistics

Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined by the q-logarithm and the q-exponential functions to the definition of the likelihood function in Gauss' law of error. The maximum likelihood principle leads us to finding Tsallis distribution as nonextensively generalization of Gaussian distribution.

cond-mat.stat-mech↗