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Title: K-theoretic classification of canonical Z2-actions on certain purely infinite Cx-algebras
Author: Goldstein, P.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 1997
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Canonical Z2-actions on certain C*-algebras are investigated. The algebras under consideration are C* -algebras on generators and relations associated to directed graphs, and, depending on the graph, they are shown to be either AF or purely infinite and simple. The class of graph C* -algebras contains Cuntz-Krieger algebras OA and the Cuntz algebra O, and can be regarded as a generalisation of those, corresponding to countably infinite matrices. Dynamical systems of the form (OA, α), where OA is an even Cuntz-Krieger algebra, and α the above canonical symmetry, are considered. If the pair (OA, α) satisfies certain conditions, it is shown to be classified by the following K-theoretic invariant: The proof uses the Rokhlin property of the canonical endomorphism on OA. It is shown that such a pair (OA, α) is isomorphic to the inductive limit system lim (An, αn), where each An is a direct sum of matrix algebras over even Cuntz algebras, and αn the canonical symmetry. Dynamical systems of the form (O, α) and (Oβ) are isomorphic. The proof is based on the corresponding results for the actions on Cuntz algebras, and approximate absorption.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available