## Tokyo Journal of Mathematics

### Properties of Topological Dynamical Systems and Corresponding $C^*$-Algebras

#### Abstract

We show the equivalence of a certain property of topological dynamical systems $\Sigma=(X,G)$ and a particular structure of ideals in the corresponding crossed product $A(\Sigma)=C(X)\underset{\alpha}{\rtimes}G$ where $X$ is a compact set and $G$ is a discrete group. As an application, we give a complete characterization for $A(\Sigma)$ to be simple.

#### Article information

Source
Tokyo J. of Math. Volume 13, Number 2 (1990), 251-257.

Dates
First available in Project Euclid: 1 April 2010

Permanent link to this document
http://projecteuclid.org/euclid.tjm/1270132260

Digital Object Identifier
doi:10.3836/tjm/1270132260

Mathematical Reviews number (MathSciNet)
MR1088230

Zentralblatt MATH identifier
0724.54037

#### Citation

KAWAMURA, Shinzô; TOMIYAMA, Jun. Properties of Topological Dynamical Systems and Corresponding $C^*$-Algebras. Tokyo J. of Math. 13 (1990), no. 2, 251--257. doi:10.3836/tjm/1270132260. http://projecteuclid.org/euclid.tjm/1270132260.