Pseudo-multiplicative unitaries and pseudo-Kac systems on C*-modules [Elektronische Ressource] / vorgelegt von Thomas Timmermann

MathematikDissertationsthemaPseudo-multiplicative unitariesand pseudo-Kac systemsonC -modulesInaugural-Dissertationzur Erlangung des Doktorgradesder Naturwissenschaften im FachbereichMathematik und Informatikder Mathematisch-Naturwissenschaftlichen Fakult atder Westf alischen Wilhelms-Universit at Munstervorgelegt vonThomas Timmermannaus Leipzig-2005-Dekan: Prof. Dr. Klaus HinrichsErster Gutachter: Prof. Dr. Joachim CuntzZweiter Gutachter: Prof. Dr. Siegfried Echterho Tag der mundlic hen Prufung: 30.06.2005Tag der Promotion: 13.07.2005AbstractWe study pseudo-multiplicative unitaries and pseudo-Kac systems on C -modules in general and examples arising from locally compact groupoids in par-ticular. Multiplicative unitaries on Hilbert spaces were introduced by Saad Baajand Georges Skandalis as a framework for generalisations of Pontrjagin duality oflocally compact abelian groups: each locally compact quantum group gives riseto a multiplicative unitary from which one can construct two Hopf C -algebrasrepresenting the initial quantum group and its generalised Pontrjagin dual [3, 28].Building on the notion of a Kac system, they de ne reduced crossed products forcoactions of Hopf C -algebras and prove a generalisation of the Takesaki-Takaiduality theorem [3].