Abstract
We construct a class of compact quantum metric spaces. We prove that twisted reduced group C*-algebras for discrete groups with twisted rapid decay property are compact quantum metric spaces, which contain noncommutative tori, hyperbolic reduced group C*-algebras and discrete Heisenberg group C*-algebras, and that the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.
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