Browsing Mathematics Theses and Dissertations by Author "Buck, Julian Michael, 1982"
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Crossed product C*algebras of certain nonsimple C*algebras and the tracial quasiRokhlin propertyBuck, Julian Michael, 1982 (University of Oregon, June , 2010)[more][less]Buck, Julian Michael, 1982 20101130T23:48:55Z 20101130T23:48:55Z 201006 http://hdl.handle.net/1794/10849 viii, 113 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 four principal parts. In the first, we introduce the tracial quasiRokhlin property for an automorphism α of a C *algebra A (which is not assumed to be simple or to contain any projections). We then prove that under suitable assumptions on the algebra A , the associated crossed product C *algebra C *([Special characters omitted.] , A , α) is simple, and the restriction map between the tracial states of C *([Special characters omitted.] , A , α) and the αinvariant tracial states on A is bijective. In the second part, we introduce a comparison property for minimal dynamical systems (the dynamic comparison property) and demonstrate sufficient conditions on the dynamical system which ensure that it holds. The third part ties these concepts together by demonstrating that given a minimal dynamical system ( X, h ) and a suitable simple C *algebra A , a large class of automorphisms β of the algebra C ( X, A ) have the tracial quasiRokhlin property, with the dynamic comparison property playing a key role. Finally, we study the structure of the crossed product C *algebra B = C *([Special characters omitted.] , C ( X , A ), β) by introducing a subalgebra B { y } of B , which is shown to be large in a sense that allows properties B { y } of to pass to B . Several conjectures about the deeper structural properties of B { y } and B are stated and discussed. Committee in charge: Christopher Phillips, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Huaxin Lin, Member, Mathematics; Marcin Bownik, Member, Mathematics; Van Kolpin, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Dynamical systems Minimal homeomorphisms Crossed product algebras Tracial property Automorphisms C*algebras QuasiRokhlin property Mathematics Theoretical mathematics Crossed product C*algebras of certain nonsimple C*algebras and the tracial quasiRokhlin property Thesis
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