Commuting algebraic correspondences and groups
type: Item
instance of: scholarly article
title: Commuting algebraic correspondences and groups
zbMATH Open document ID: 0921.58020
DOI: 10.1007/BF02355075
author: I. V. Zefirov
published in: Mathematical Notes
publication date: 1999-09-26T00:00:00Z
review text: The naturalness of the appearance of the group approach in the study of the problems of algebraic commutation is considered. The present paper is devoted to the case of multivalued algebraic mappings or correspondences \(x\rightarrow y_i\), which is given by solutions of a polynomial equation \(P(x,y)=0\). In the case of algebraic correspondences, only a few examples of commutations are known. The author constructs a new example of a commuting algebraic correspondence and suggests a group approach to construction of other similar examples from the icosahedral equation. The interest to these examples stems from the theory of dynamical systems and possible applications in the theory of integral models of statistical mechanics.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 1238042
zbMATH Keywords: commutation
zbMATH Keywords: algebraic correspondence
zbMATH Keywords: symmetric correspondence
zbMATH Keywords: icosahedral group
MaRDI profile type: Publication
cites work: Q3363790
cites work: Q5583892
description: scientific article; zbMATH DE number 1238042