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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorExterne beoordelaar - External assesor,
dc.contributor.authorVries, Jens de
dc.date.accessioned2022-06-10T00:00:42Z
dc.date.available2022-06-10T00:00:42Z
dc.date.issued2022
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/41625
dc.description.abstractThe study of classical dynamical systems deals with actions of locally compact Hausdorff groups on locally compact Hausdorff spaces. It is long recognized that classical dynamical systems can be studied successfully via C*-algebras. A C*-action is a strongly continuous group homomorphism from a locally compact Hausdorff group to the automorphism group of a C*-algebra. The C*-actions involving the commutative C*-algebras precisely model the classical dynamical systems. Every C*-action gives rise to a C*-algebra, called the crossed product, which encodes a lot of information about the C*-action. Using crossed products and duality theory for abelian locally compact Hausdorff groups one can develop a certain duality theory for C*-actions. Just as Pontryagin duality describes the second dual of a topological group, Takai duality describes the second dual of a C*-action. The idea is that one recovers a C*-action from its crossed product up to tensoring with another C*-action.
dc.description.sponsorshipUtrecht University
dc.language.isoEN
dc.subjectThis thesis provides a more accessible proof of the Takai duality theorem. The Takai duality theorem recovers a crossed product from its C*-action up to tensoring with another C*-action.
dc.titleC*-Actions and Takai Duality
dc.type.contentMaster Thesis
dc.rights.accessrightsOpen Access
dc.subject.keywordsC*-algebra; C*-action; dynamical system; Takai duality; topological group; operator algebra; Stone-Neumann theorem; Pontryagin duality; functional analysis; crossed product; covariant representation;
dc.subject.courseuuMathematical Sciences
dc.thesis.id4336


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