$C^{\ast}$-Algebras associated with Mauldin-Williams Graphs
| dc.creator | Ionescu, Marius | |
| dc.creator | Watatani, Yasuo | |
| dc.date | 2004-10-22 | |
| dc.date | 2005-01-19 | |
| dc.date.accessioned | 2026-07-07T05:13:36Z | |
| dc.date.available | 2026-07-07T05:13:36Z | |
| dc.description | A Mauldin-Williams graph $\mathcal{M}$ is a generalization of an iterated function system by a directed graph. Its invariant set $K$ plays the role of the self-similar set. We associate a $C^{*}$-algebra $\mathcal{O}_{\mathcal{M}}(K)$ with a Mauldin-Williams graph $\mathcal{M}$ and the invariant set $K$ laying emphasis on the singular points. We assume that the underlying graph $G$ has no sinks and no sources. If $\mathcal{M}$ satisfies the open set condition in $K$ and $G$ is irreducible and is not a cyclic permutation, then the associated $C^{*}$-algebra $\mathcal{O}_{\mathcal{M}}(K)$ is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the Penrose tilings. | |
| dc.description | 14 pages, Latex, 4 figures. We added new references and did minor changes in the introduction | |
| dc.identifier | https://arxiv.org/abs/math/0410480 | |
| dc.identifier | http://arxiv.org/abs/math/0410480 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72967 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.title | $C^{\ast}$-Algebras associated with Mauldin-Williams Graphs | |
| dc.type | text |