C^*-algebras associated with self-similar sets

Details C^*-algebras associated with self-similar sets C^*-algebras associated with self-similar sets

2003-12-29

arxiv.org/abs/math/0312481v2

Mathematics

Operator Algebras

22 pages: Corrected Version

Scientific paper

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N \{(x,y) \in K^2 ; x = \gamma_i(y)\}$ of the cographs of \gamma _i$. Then $X = C({\mathcal G})$ is a Hilbert bimodule over $A = C(K)$. We associate a $C^*$-algebra ${\mathcal O}_{\gamma}(K)$ with them as a Cuntz-Pimsner algebra ${\mathcal O}_X$. We show that if a system of proper contractions satisfies the open set condition in $K$, then the $C^*$-algebra ${\mathcal O}_{\gamma}(K)$ is simple and purely infinite, which is not isomorphic to a Cuntz algebra in general.

Affiliated with

Also associated with

No associations

Rating

C^*-algebras associated with self-similar sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with C^*-algebras associated with self-similar sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and C^*-algebras associated with self-similar sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-717714