Commuting algebraic correspondences and groups (Q1274082)

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.