C*-algebras associated with Mauldin-Williams graphs

Marius Ionescu, Yasuo Watatani

研究成果: Contribution to journalArticle査読

6 被引用数 (Scopus)

抄録

A Mauldin-Williams graph 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 OM (K) with a Mauldin-Williams graph 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 M satisfies the open set condition in K, and G is irreducible and is not a cyclic permutation, then the associated C*-algebra OM (K) is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the Penrose tilings.

本文言語英語
ページ(範囲)545-560
ページ数16
ジャーナルCanadian Mathematical Bulletin
51
4
DOI
出版ステータス出版済み - 12 2008

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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