On amenable semigroups of rational functions

Fedor Pakovich

doi:10.1090/tran/8731

On amenable semigroups of rational functions

Fedor Pakovich

Department of Mathematics

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Abstract

We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular, we show that under quite general conditions a semigroup of rational functions is amenable if and only if it is a subsemigroup of the centralizer of some rational function.

Original language	English
Pages (from-to)	7945-7979
Number of pages	35
Journal	Transactions of the American Mathematical Society
Volume	375
Issue number	11
DOIs	https://doi.org/10.1090/tran/8731
State	Published - 1 Nov 2022

Keywords

math.DS
math.CV

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/tran/8731

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N2 - We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular, we show that under quite general conditions a semigroup of rational functions is amenable if and only if it is a subsemigroup of the centralizer of some rational function.

AB - We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular, we show that under quite general conditions a semigroup of rational functions is amenable if and only if it is a subsemigroup of the centralizer of some rational function.

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JF - Transactions of the American Mathematical Society

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On amenable semigroups of rational functions

Abstract

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