Twisted Group C *-Algebras as Compact Quantum Metric Spaces

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.