Skip to main content
SpringerLink
Log in

A note on quantum odometers

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

We discuss various aspects of noncommutative geometry of smooth subalgebras of Bunce-Deddens-Toeplitz algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blackadar B, Cuntz J. Differential Banach algebra norms and smooth subalgebras of C*-algebras. J Operator Theory, 1991, 26: 255–282

    MathSciNet  MATH  Google Scholar 

  2. Bost J-B. Principe d’Oka, K-théorie et systèmes dynamiques non commutatifs. Invent Math, 1990, 101: 261–333

    Article  MathSciNet  MATH  Google Scholar 

  3. Bunce J W, Deddens J A. C*-algebras generated by weighted shifts. Indiana Univ Math J, 1973, 23: 257–271

    Article  MathSciNet  MATH  Google Scholar 

  4. Bunce J W, Deddens J A. A family of simple C*-algebras related to weighted shift operators. J Funct Anal, 1975, 19: 13–24

    Article  MathSciNet  MATH  Google Scholar 

  5. Connes A. Non-Commutative Differential Geometry. Boston: Academic Press, 1994

    MATH  Google Scholar 

  6. Downarowicz T. Survey of odometers and Toeplitz flows. Contemp Math, 2005, 385: 7–37

    Article  MathSciNet  MATH  Google Scholar 

  7. Klimek S, McBride M. Unbounded derivations in algebras associated with monothetic groups. J Aust Math Soc, 2021, 111: 345–371

    Article  MathSciNet  MATH  Google Scholar 

  8. Klimek S, McBride M, Peoples J W. Aspects of noncommutative geometry of Bunce-Deddens algebras. arXiv: 2112.00572, 2021

  9. Klimek S, McBride M, Peoples J W. Noncommutative geometry of the quantum disk. Ann Funct Anal, 2022, 13: 53

    Article  MathSciNet  MATH  Google Scholar 

  10. Klimek S, McBride M, Rathnayake S, et al. Unbounded derivations in Bunce-Deddens-Toeplitz algebras. J Math Anal Appl, 2019, 474: 988–1020

    Article  MathSciNet  MATH  Google Scholar 

  11. Phillips N C. K-theory for Fréchet algebras. Internat J Math, 1991, 2: 77–129

    Article  MathSciNet  MATH  Google Scholar 

  12. Rordam M, Larsen F, Lausten N J. An Introduction to K-Theory for C*-Algebras. Cambridge: Cambridge University Press, 2000

    Book  Google Scholar 

  13. Rosenberg J, Schochet C. The Kunneth theorem and the universal coefficient theorem for Kasporov’s generalised K-functor. Duke Math J, 1987, 55: 431–474

    Article  MathSciNet  MATH  Google Scholar 

  14. Sakai S. Operator Algebras in Dynamical Systems. Cambridge: Cambridge University Press, 1991

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN, 46202, USA

    Slawomir Klimek

  2. Department of Mathematics and Statistics, Mississippi State University, Starkville, Mississippi State, MS, 39762, USA

    Matt McBride

  3. Department of Mathematics, The Pennsylvania State University, University Park, State College, PA, 16802, USA

    J. Wilson Peoples

Authors
  1. Slawomir Klimek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matt McBride
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Wilson Peoples
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matt McBride.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klimek, S., McBride, M. & Peoples, J.W. A note on quantum odometers. Sci. China Math. 66, 1555–1568 (2023). https://doi.org/10.1007/s11425-022-2012-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-022-2012-7

Keywords

MSC(2020)

Search

Navigation