C*-algebras associated with interval maps
Abstract
For each piecewise monotonic map tau of [0,1], we associate a pair of C*-algebras F_tau and O_tau and calculate their K-groups. The algebra F_tau is an AI-algebra. We characterize when F_tau and O_\tau are simple. In those cases, F_tau has a unique trace, and O_tau is purely infinite with a unique KMS-state. In the case that tau is Markov, these algebras include the Cuntz-Krieger algebras O_A, and the associated AF-algebras F_A. 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 O_tau coincides with the algebras defined by Putnam and Katayama-Matsumoto-Watatani respectively.
Keywords
Cite
@article{arxiv.math/0405469,
title = {C*-algebras associated with interval maps},
author = {Valentin Deaconu and Fred Shultz},
journal= {arXiv preprint arXiv:math/0405469},
year = {2007}
}
Comments
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