Some intrinsic properties of simple graph $C^*$-algebras

Details Some intrinsic properties of simple graph $C^*$-algebras Some intrinsic properties of simple graph $C^*$-algebras

2002-12-18

arxiv.org/abs/math/0212242v1

Mathematics

Operator Algebras

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

Scientific paper

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

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