Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus

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Title: Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus
Author: Sun, Wei, 1979-
Abstract: This dissertation is a study of the relationship between minimal dynamical systems on the product of the Cantor set ( X ) and torus ([Special characters omitted]) and their corresponding crossed product C *-algebras. For the case when the cocyles are rotations, we studied the structure of the crossed product C *-algebra A by looking at a large subalgebra A x . It is proved that, as long as the cocyles are rotations, the tracial rank of the crossed product C *-algebra is always no more than one, which then indicates that it falls into the category of classifiable C *-algebras. In order to determine whether the corresponding crossed product C *-algebras of two such minimal dynamical systems are isomorphic or not, we just need to look at the Elliott invariants of these C *-algebras. If a certain rigidity condition is satisfied, it is shown that the crossed product C *-algebra has tracial rank zero. Under this assumption, it is proved that for two such dynamical systems, if A and B are the corresponding crossed product C *-algebras, and we have an isomorphism between K i ( A ) and K i ( B ) which maps K i (C(X ×[Special characters omitted])) to K i (C( X ×[Special characters omitted])), then these two dynamical systems are approximately K -conjugate. The proof also indicates that C *-strongly flip conjugacy implies approximate K -conjugacy in this case. We also studied the case when the cocyles are Furstenberg transformations, and some results on weakly approximate conjugacy and the K -theory of corresponding crossed product C *-algebras are obtained.
Description: vii, 124 p. : ill. 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/1794/10912
Date: 2010-06


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