C*-algebras associated with self-similar sets

Tsuyoshi Kajiwara, Yasuo Watatani

研究成果: Contribution to journalArticle査読

10 被引用数 (Scopus)

抄録

Let γ = (γ1,..., γN), N ≥ 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 G = ∪i=1N {(x,y) ∈ K2;x = γi(y)} of the cographs of γi. Then X = C(G) is a Hilbert bimodule over A = C(K). We associate a C*-algebra script O signγ(K) with them as a Cuntz-Pimsner algebra script O signX. We show that if a system of proper contractions satisfies the open set condition in K, then the C*-algebra script O sign γ(K) is simple, purely infinite and, in general, not isomorphic to a Cuntz algebra.

本文言語英語
ページ(範囲)225-247
ページ数23
ジャーナルJournal of Operator Theory
56
2
出版ステータス出版済み - 9 1 2006

All Science Journal Classification (ASJC) codes

  • 代数と数論

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