Crossed product C*-algebras of certain non-simple C*-algebras and the tracial quasi-Rokhlin property
Loading...
Date
2010-06
Authors
Buck, Julian Michael, 1982-
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
This dissertation consists of four principal parts. In the first, we introduce the tracial quasi-Rokhlin 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 α-invariant 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 quasi-Rokhlin 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.
Description
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.
Keywords
Dynamical systems, Minimal homeomorphisms, Crossed product algebras, Tracial property, Automorphisms, C*-algebras, Quasi-Rokhlin property, Mathematics, Theoretical mathematics