Skip to main content

Reduced C*-algebras of discrete groups which are simple with a unique trace

Part of the Lecture Notes in Mathematics book series (LNM,volume 1132)

Keywords

  • Free Product
  • Finite Subset
  • Finite Index
  • Hyperbolic Element
  • Hausdorff Topological Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C.A. Akemann and T.Y. Lee: "Some simple C*-algebras associated with free groups". Indiana Math. J. 29 (1980) 505–511.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. R.J. Archbold: "On the Dixmier property of certain algebras". Math. Proc. Camb. Phil. Soc. 86 (1979) 251–259.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. P. Baum and A. Connes: "Geometric K theory for Lie groups and foliations". Preprint, November 1982.

    Google Scholar 

  4. H. Bass: "Groups of integral representation type". Pacific J. Math. 86 (1980) 15–51.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. H. Bass: "Euler characteristics and characters of discrete groups". Invent. Math. 35 (1976) 155–196.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. E. Bédos: "Operator algebras associated with free products of groups with amalgamation". Preprint, Oslo 1982.

    Google Scholar 

  7. E. Bédos: "Operator algebras associated with HNN-extensions". Preprint, Oslo 1983.

    Google Scholar 

  8. K. Bonvallet, B. Hartley, D.S. Passman and M.K. Smith: "Group rings with simple augmentation ideals". Proc. Amer. Math. Soc. 56 (1976) 79–82.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. P. Eberlein and B. O’Neill: "Visibility manifolds". Pacific J. Math. 46 (1973) 45–109.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. E. Formanek: "Idempotents in noetherian group rings". Can. J. Math. 25 (1973) 366–369.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. M. Gromov: "Groups of polynomial growth and expanding maps". Publ. Math. IHES 53 (1981) 53–78.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. P. de la Harpe and K. Jhabvala: "Quelques propriétés des algèbres d’un groupe discontinu d’isométries hyperboliques". Monographie 29 in l’Enseignement math. (1981) 47–55.

    MATH  Google Scholar 

  13. P. de la Harpe: "Free groups in linear groups". L’Enseignement math. 29 (1983) 129–144.

    MathSciNet  MATH  Google Scholar 

  14. R.V. Kadison, E.C. Lance and J.R. Ringrose: "Derivations and automorphisms of operator algebras II". J. Functional anal. 1 (1967) 204–221.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R.C. Lyndon and P.E. Schupp: "Combinatorial group theory". Springer 1977.

    Google Scholar 

  16. A.I. Mal’cev: "On the faithful representations of infinite groups by matrices". Amer. Math. Soc. Transl. (2) 45 (1965) 1–18.

    CrossRef  MathSciNet  Google Scholar 

  17. G.D. Mostow: "Strong rigidity of locally symmetric spaces". Princeton Univ. Press 1973.

    Google Scholar 

  18. W.L. Paschke and N. Salinas: "C*-algebras associated with free products of groups". Pacific J. Math. 82 (1979) 211–221.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. D.S. Passmann: "The algebraic structure of group rings". Wiley Interscience 1977.

    Google Scholar 

  20. G.K. Pedersen: "C*-algebras and their automorphism groups". Academic Press 1979.

    Google Scholar 

  21. R.T. Powers: "Simplicity of the C*-algebra associated with the free group on two generators". Duke Math. J. 42 (1975) 151–156.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. G. Prasad and M.S. Raghunathan: "Cartan subgroups and lattices in semi-simple groups". Ann. of Math. 96 (1972) 296–317.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. M.S. Raghunathan: "Discrete subgroups of Lie groups". Springer 1972.

    Google Scholar 

  24. J.P. Serre: "Arbres, amalgames, SL2". Astérisque 46 (Soc. Math. France 1977).

    MATH  Google Scholar 

  25. J. Tits: "Free subgroups in linear groups". J. of Algebra 20 (1972) 250–270.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. B.A.F. Wehrfritz: "2-generator conditions in linear groups". Archiv. Math. 22 (1971) 237–240.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verleg

About this paper

Cite this paper

de la Harpe, P. (1985). Reduced C*-algebras of discrete groups which are simple with a unique trace. In: Araki, H., Moore, C.C., Stratila, ŞV., Voiculescu, DV. (eds) Operator Algebras and their Connections with Topology and Ergodic Theory. Lecture Notes in Mathematics, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074887

Download citation

  • DOI: https://doi.org/10.1007/BFb0074887

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15643-7

  • Online ISBN: 978-3-540-39514-0

  • eBook Packages: Springer Book Archive