2004/05/24 by Valentin Deaconu, Deaconu, Valentin, Fred Shultz +1
Computer Science · Mathematics · #46L80 (primary) 37E05 (secondary) #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #math.DS #math.OA #msc:37E05 #msc:46L80
paper · pdf · doi:10.48550/arxiv.math/0405469
35 pages, 1 eps figure, LateX. Editorial changes, and shortened for publication by omitting previous sections 8, 9 and revising introduction. Has been accepted for publication in the AMS Transactions
openalex publication_date 2004/05/24 · arxiv created 2005/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For each piecewise monotonic map tau of [0,1], we associate a pair of C*-algebras Ftau and Otau and calculate their K-groups. The algebra Ftau is an AI-algebra. We characterize when Ftau and Oτare simple. In those cases, Ftau has a unique trace, and Otau is purely infinite with a unique KMS-state. In the case that tau is Markov, these algebras include the Cuntz-Krieger algebras OA, and the associated AF-algebras FA. Other examples for which the K-groups are computed include tent maps, quadratic maps, multimodal maps, interval exchange maps, and beta-transformations. For the case of interval exchange maps and of beta-transformations, the C*-algebra Otau coincides with the algebras defined by Putnam and Katayama-Matsumoto-Watatani respectively.