Hyperbolic Group C * -algebras and Free-product C * -algebras as Compact Quantum Metric Spaces

@inproceedings{Rieffel2008HyperbolicGC,
  title={Hyperbolic Group C * -algebras and Free-product C * -algebras as Compact Quantum Metric Spaces},
  author={Marc Rieffel},
  year={2008}
}
Let l be a length function on a group G, and let Ml denote the operator of pointwise multiplication by l on l(G). Following Connes, Ml can be used as a “Dirac” operator for C ∗ r (G). It defines a Lipschitz seminorm on C∗ r (G), which defines a metric on the state space of C∗ r (G). We show that if G is a hyperbolic group and if l is a word-length function on G, then the topology from this metric coincides with the weak-∗ topology (our definition of a “compact quantum metric space”). We show… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 15 references

Compact metric spaces, Fredholm modules, and hyperfiniteness

  • A. Connes
  • Ergodic Theory Dynamical Systems,
  • 1989
Highly Influential
7 Excerpts

On the existence of quasicentral approximate units relative to normed ideals

  • D. Voiculescu
  • Part I. J. Funct. Anal
  • 1990
Highly Influential
3 Excerpts

Sur les groupes hyperboliques d’après Mikhael Gromov

  • É. Ghys, P. de la Harpe, editors
  • 1990
Highly Influential
3 Excerpts

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