Matrix homomorphism equations on a class of monoids and non abelian groupoids
type: Item
instance of: scholarly article
title: Matrix homomorphism equations on a class of monoids and non abelian groupoids
zbMATH Open document ID: 1473.39040
author: A. Mouzoun
author: Driss Zeglami
author: Y. Aissi
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-07-23T00:00:00Z
review text: The authors present an explicit description of the solutions \(f : \mathbb{R}^2 \to M_2(\mathbb{C})\) of the parametric functional equation \[f(x_1x_2 + \alpha y_1y_2, x_1y_2 + \beta x_2y_1) = f(x_1, y_1)f(x_2, y_2),\] where \(\alpha, \beta\in \mathbb{R}\). They explore the solutions of a matrix multiplicative Cauchy functional equation on abelian regular semigroups. As an application, they characterize the solution \(f : \mathbb{R}^2 \to M_2(\mathbb{C})\) of matrix functional equation \[f(x_1x_2 + \alpha y_1y_2, x_1y_2 + \beta x_2y_1) = f(x_1, y_1) + f(x_2, y_2) + \lambda f(x_1, y_1)f(x_2, y_2),\] where \(\lambda\in \mathbb{C}\).
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 39B42
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 7374596
zbMATH Keywords: matrix functional equation
zbMATH Keywords: number theory
zbMATH Keywords: homomorphism
zbMATH Keywords: multiplicative function
zbMATH Keywords: groupoid
zbMATH Keywords: linear algebra
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125354
OpenAlex ID: W3162424169
cites work: Q3992445
cites work: D'Alembert's matrix functional equation with an endomorphism on abelian groups
cites work: A functional equation related to the product in a quadratic number field
cites work: On functional equations of the multiplicative type
cites work: Reconsidering a functional equation arising from number theory
cites work: D'Alembert's other functional equation on monoids with an involution
cites work: On two functional equations and their solutions
cites work: Some functional equations originating from number theory
cites work: Functional Equations and Inequalities with Applications
cites work: Functional equations on abelian groups with involution
cites work: D'Alembert's and Wilson's functional equations for vector and $2\times 2$ matrix valued functions
cites work: Some functional equations related to number theory
DOI: 10.1016/J.JMAA.2021.125354
Recommended article: Q3149111
Recommended article: Semigroup homomorphisms on matrix algebras
Recommended article: Matrix groupoids
Recommended article: The classification of maximal inverse monoids of matrices
Recommended article: Homomorphisms between multiplicative semigroups of matrices over fields.
Recommended article: Q5287828
Recommended article: Difference matrices and orthomorphisms over non-abelian groups
Recommended article: Homomorphisms of \(\ell ^1\)-Munn algebras and Rees matrix semigroup algebras
Recommended article: Group algebras and enveloping algebras with nonmatrix and semigroup identities
Recommended article: More on matrix semigroup homomorphisms
description: scientific article; zbMATH DE number 7374596