C^*-algebras associated with self-similar sets
| dc.creator | Kajiwara, Tsuyoshi | |
| dc.creator | Watatani, Yasuo | |
| dc.date | 2003-12-29 | |
| dc.date | 2004-03-25 | |
| dc.date.accessioned | 2026-07-07T05:04:14Z | |
| dc.date.available | 2026-07-07T05:04:14Z | |
| dc.description | Let $γ= (γ_1,...,γ_N)$, $N \geq 2$, 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 ${\mathcal G} = \cup_{i=1}^N \{(x,y) \in K^2 ; x = γ_i(y)\}$ of the cographs of γ_i$. Then $X = C({\mathcal G})$ is a Hilbert bimodule over $A = C(K)$. We associate a $C^*$-algebra ${\mathcal O}_γ(K)$ 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 ${\mathcal O}_γ(K)$ is simple and purely infinite, which is not isomorphic to a Cuntz algebra in general. | |
| dc.description | 22 pages: Corrected Version | |
| dc.identifier | https://arxiv.org/abs/math/0312481 | |
| dc.identifier | http://arxiv.org/abs/math/0312481 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69725 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | 46L08, 46L80 | |
| dc.title | C^*-algebras associated with self-similar sets | |
| dc.type | text |