The tracial Rokhlin property for automorphisms on non-simple C*-algebras

Abstract

Let A be a unital AF-algebra (simple or non-simple) and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that α J * 0 =id K 0 (A) . The author proves that A α Z has tracial rank zero.

Certain properties for crossed products by automorphisms with a certain non-simple tracial Rokhlin property

“…In [11] Hua introduced a certain tracial Rokhlin property for non-simple C * -algebras with an action of the group Z, the analogous tracial Rokhlin property for non-simple C *algebras to that defined by Hua for an action of a finite group, given by Yang and Fang in [21].…”

“…[11,21] Let A be a unital C * -algebra. [11,21] Let A be a unital C * -algebra with the property SP and let α : G → Aut(A) be an action of a finite group G on A which has the tracial Rokhlin property. Suppose that A is α-simple.…”

“…In [11] Hua introduced a certain Rokhlin property for non-simple C * -algebras. In [11] Hua introduced a certain Rokhlin property for non-simple C * -algebras.…”