Mathematics, Department of
Department of Mathematics: Dissertations, Theses, and Student Research
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First Advisor
David R. Pitts
Date of this Version
Spring 5-2015
Document Type
Dissertation
Abstract
We develop the property of Invariant Basis Number (IBN) in the context of C*-algebras and their Hilbert modules. A complete K-theoretic characterization of C*- algebras with IBN is given. A scheme for classifying C*-algebras which do not have IBN is given and we prove that all such classes are realized. We investigate the invariance of IBN, or lack thereof, under common C*-algebraic construction and perturbation techniques. Finally, applications of Invariant Basis Number to the study of C*-dynamical systems and the classification program are investigated.
Adviser: David Pitts
Included in
Algebra Commons, Analysis Commons, Other Mathematics Commons
Comments
A dissertation Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor David Pitts. Lincoln, Nebraska: May, 2015
Copyright (c) 2015 Philip Melvin Gipson