Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus
| dc.contributor.author | Sun, Wei, 1979- | |
| dc.date.accessioned | 2010-12-22T01:32:21Z | |
| dc.date.available | 2010-12-22T01:32:21Z | |
| dc.date.issued | 2010-06 | |
| dc.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. | en_US |
| dc.description.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. | en_US |
| dc.description.sponsorship | Committee in charge: Huaxin Lin, Chairperson, Mathematics Daniel Dugger, Member, Mathematics; Christopher Phillips, Member, Mathematics; Arkady Vaintrob, Member, Mathematics; Li-Shan Chou, Outside Member, Human Physiology | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/10912 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | University of Oregon | en_US |
| dc.relation.ispartofseries | University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; | |
| dc.subject | Tracial rank | en_US |
| dc.subject | Approximate conjugacy | en_US |
| dc.subject | C*-algebras | en_US |
| dc.subject | Minimal dynamical systems | en_US |
| dc.subject | Cantor set | en_US |
| dc.subject | Torus | en_US |
| dc.subject | Mathematics | en_US |
| dc.subject | Theoretical mathematics | en_US |
| dc.title | Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus | en_US |
| dc.type | Thesis | en_US |
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