Ideal structure of C*-algebras of singly generated dynamical systems

TL;DR

This paper characterizes the ideal structure of C*-algebras arising from singly generated dynamical systems, establishing a bijective correspondence with certain subsets of the product space and the circle.

Contribution

It provides a complete description of the ideal lattice of these C*-algebras using a novel subset characterization.

Findings

Ideal set corresponds bijectively to specific subsets of the product space and circle

Provides a new framework for understanding the structure of C*-algebras from dynamical systems

Enhances classification methods for these C*-algebras

Abstract

In this paper, we show that the set of all ideals of the C*-algebras of a singly generated dynamical system corresponds bijectively to the set of all subsets of the product of the space of the system and the circle satisfying three conditions.