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

  title={Hyperbolic Group C * -algebras and Free-product C * -algebras as Compact Quantum Metric Spaces},
  author={Marc Rieffel},
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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