Browsing Mathematics Theses and Dissertations by Author "Liang, Hutian"
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Liang, Hutian (University of Oregon, June , 2010)[more][less]Liang, Hutian 20110114T18:44:40Z 20110114T18:44:40Z 201006 http://hdl.handle.net/1794/10938 viii, 133 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. In this dissertation, we will study the crossed product C*algebras obtained from free and minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. We first define stable recursive subhomogeneous algebras (SRSHAs), which differ from recursive subhomogeneous algebras introduced by N. C. Phillips in that the irreducible representations of SRSHAs are infinite dimensional instead of finite dimensional. We show that simple inductive limits of SRSHAs with no dimension growth in which the connecting maps are injective and nonvanishing have topological stable rank one. We then construct C*subalgebras of the crossed product that are analogous to the C*subalgebras in the studies of free minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. Finally, we prove that these C*algebras are in fact simple inductive limits of SRSHAs in which the connecting maps are injective and nonvanishing. Thus these C*subalgebras have topological stable rank one. Committee in charge: Christopher Phillips, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Huaxin Lin, Member, Mathematics; Yuan Xu, Member, Mathematics; Dietrich Belitz, Outside Member, Physics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Free minimal action Metric space Subhomogeneous algebras Infinite dimensions Topological stability Mathematics Theoretical mathematics The crossed product of C(X) by a free minimal action of R Thesis
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