The C*-algebra of the exponential function

TL;DR

This paper investigates the C*-algebra associated with the complex exponential function and its conjugate, deriving explicit descriptions based on their properties as local homeomorphisms and étale groupoids.

Contribution

It explicitly determines the C*-algebra generated by the exponential function and its conjugate, expanding understanding of their algebraic structures.

Findings

Explicit description of the C*-algebra for the exponential function

Analysis of the C*-algebra for the conjugate exponential function

Connection between local homeomorphism properties and algebraic structures

Abstract

The complex exponential function is a local homeomorphism and gives therefore rise to an 'etale groupoid and a C*-algebra. We determine this algebra, as well as the alge bra of the complex conjugate of the exponential function.