Crossed product C*-algebras by finite group actions with a generalized tracial Rokhlin property

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Title: Crossed product C*-algebras by finite group actions with a generalized tracial Rokhlin property
Author: Archey, Dawn Elizabeth, 1979-
Abstract: This dissertation consists of two related parts. In the first portion we use the tracial Rokhlin property for actions of a finite group G on stably finite simple unital C *-algebras containing enough projections. The main results of this part of the dissertation are as follows. Let A be a stably finite simple unital C *-algebra and suppose a is an action of a finite group G with the tracial Rokhlin property. Suppose A has real rank zero, stable rank one, and suppose the order on projections over A is determined by traces. Then the crossed product algebra C * ( G, A, à à ±) also has these three properties. In the second portion of the dissertation we introduce an analogue of the tracial Rokhlin property for C *-algebras which may not have any nontrivial projections called the projection free tracial Rokhlin property . Using this we show that under certain conditions if A is an infinite dimensional simple unital C *-algebra with stable rank one and à à ± is an action of a finite group G with the projection free tracial Rokhlin property, then C * ( G, A, à à ±) also has stable rank one.
Description: viii, 107 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
URI: http://hdl.handle.net/1794/8155
Date: 2008-06


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