Stable and Real Rank for Crossed Products by Automorphisms with the Tracial Rokhlin Property
نویسندگان
چکیده
We introduce the tracial Rokhlin property for automorphisms of stably finite simple unital C*-algebras containing enough projections. This property is formally weaker than the various Rokhlin properties considered by Herman and Ocneanu, Kishimoto, and Izumi. Our main results are as follows. Let A be a stably finite simple unital C*-algebra, and let α be an automorphism of A which has the tracial Rokhlin property. Suppose A has real rank zero and stable rank one, and suppose that the order on projections over A is determined by traces. Then the crossed product algebra C(Z, A, α) also has these three properties. We also present examples of C*-algebras A with automorphisms α which satisfy the above assumptions, but such that C(Z, A, α) does not have tracial rank zero.
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