Skip to main content

Free Products of Exact Groups

  • Conference paper
C*-Algebras

Abstract

It has recently been proved that the class of unital exact C*-algebras is closed under taking reduced amalgamated free products. Here the proof is presented of a special case: that the class of exact discrete groups is closed under taking free products (with amalgamation over the identity element). The proof of this special case is considerably simpler than in full generality.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Adams, Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups, Topology 33 (1994), 765–783.

    Article  MathSciNet  MATH  Google Scholar 

  2. M.-D. Choi, A simple C*-algebra genereated by two finite-order unitaries, Canad. J. Math. 31 (1979), 867–880.

    Article  MathSciNet  MATH  Google Scholar 

  3. K.J. Dykema, Exactness of reduced amalgamated free products of C* -algebras, preprint (1999).

    Google Scholar 

  4. E. Germain, Approximate invariant means for boundary actions of hyperbolic groups, appendix to Amenable Groupoids by C. Anatharaman-Delaroche and J. Renault, preprint.

    Google Scholar 

  5. P. de la Harpe, A.G. Robertson, A. Valette, On exactness of group C*-algebras, Quart. J. Math. Oxford (2) 45 (1994), 499–513.

    Article  MATH  Google Scholar 

  6. E. Kirchberg, Commutants of unitaries in UHF algebras and functorial properties of exactness, J. reine angew. Math. 452 (1994), 39–77.

    MathSciNet  MATH  Google Scholar 

  7. E. Kirchberg, S. Wasermann, Exact groups and continuous bundles of C*-algebras, preprint.

    Google Scholar 

  8. , E. Kirchberg, S. Wasermann, Permanence properties of C* -exact groups, preprint.

    Google Scholar 

  9. S. Wassermann, On tensor products of certain group C* -algebras, J. Funct. Anal. 23 (1976), 239–254.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Wassermann, Tensor products of free-group (C* -algebras, Bull. London Math. Soc. 22 (1990), 375–380.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Wassermann, Exact C*-algebras and Related Topics, Seoul National University Lecture Notes Series 19, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dykema, K.J. (2000). Free Products of Exact Groups. In: Cuntz, J., Echterhoff, S. (eds) C*-Algebras. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57288-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-57288-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67562-4

  • Online ISBN: 978-3-642-57288-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics