The Rokhlin Property for Automorphisms on Simple C-algebras
نویسنده
چکیده
We study a general Kishimoto’s problem for automorphisms on simple C∗-algebras with tracial rank zero. Let A be a unital separable simple C∗-algebra with tracial rank zero and let α be an automorphism. Under the assumption that α has certain Rokhlin property, we present a proof that A ⋊α Z has tracial rank zero. We also show that if the induced map α∗0 on K0(A) fixes a “dense” subgroup of K0(A) then the tracial Rokhlin property implies a stronger Rokhlin property. Consequently, the induced crossed product C∗-algebras have tracial rank zero.
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