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

• Main Author: Archey, Dawn Elizabeth, 1979-
• Language: en_US
• Published: University of Oregon 2008
• Subjects: Mathematics; Cuntz subequivalence; Stable rank one; Tracial Rokhlin property; Finite group actions; Crossed product; C*-algebras
• Online Access: http://hdl.handle.net/1794/8155

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. === 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. === Adviser: Phillips, N. Christopher