Some intrinsic properties of simple graph $C^{\ast }$-algebras

Abstract

To a directed graph $E$ is associated a $C^{\ast }$-algebra $C^{\ast }(E)$ called a graph $C^{\ast }$-algebra. There is a canonical action $\gamma$ of $\mathbf{T}$ on $C^{\ast }(E)$, called the gauge action. In this paper we present necessary and sufficient conditions for the fixed point algebra $C^{\ast }(E{)}^{\gamma }$ to be simple. Our results also yield some structure theorems for simple graph algebras.

15 pages with one embedded diagram. To appear, Proc. OAMP conference, Constanta, 2001

References in corpus (1)

• Graph inverse semigroups, groupoids and their C*-algebras