Course module NWI-WM140 Credits (ECTS) 6 Category MA (Master) Language of instruction English Offered by Radboud University; Faculty of Science; Wiskunde, Natuur- en Sterrenkunde; Lecturer(s) Coordinator dr. F. Arici Other course modules lecturer Contactperson for the course dr. F. Arici Other course modules lecturer Lecturer dr. F. Arici Other course modules lecturer Lecturer dr. T.G.H. Crisp Other course modules lecturer Academic year 2017 Period KW1-KW2   (04/09/2017 to 04/02/2018) Starting block KW1 Course mode full-time Remarks - Registration using OSIRIS Yes Course open to students from other faculties Yes Pre-registration No Waiting list No Placement procedure -

	Aims Students completing the course should: * become familiar with the basic theory of C*-algebras, and of the applications of this theory to the study of group representations, with particular emphasis on examples relevant to mathematical physics. * be able to construct proofs and compute examples related to course material. * acquire an in-depth knowledge of a special topic related to the core material, through the completion of an individual project. Content Introduction to C*-algebras. Introduction to locally compact groups and their representations. Group C*-algebras. Abelian C*-algebras and Pontryagin duality, Compact operators and the Peter-Weyl Theorem. The GNS construction and the Gelfand-Raikov theorem. Hilbert modules and Mackey's imprimitivity theorem. Application to group extensions, including the Poincarè group and the Heisenberg group. Test information The test consists of: * a written report, on an individual topic to be agreed upon with the lecturers; * an oral examination, based on the topic of the written report and on related content from the course. In addition to this, the students are required to complete three homework assignments throughout the semester. The final grade combines the scores from the written report (25%), oral examination (25%), and homework assignments (50%).
	Recommended materials Book K. R. Davidson, C*-algebras by examples. We will use Chapter 1 for the general theory of C*-algebras, and Chapter VII for group C*-algebras. Book G. B. Folland, A course in Abstract Harmonic Analysis This book will be used for the general theory of locally compact groups and their representations. Literature M. A. Rieffel, Induced Representations of C*_algebras, Adv. in Math. 13 (1974), 176-257. Instructional modes Course Attendance Mandatory Yes Tests Tentamen Test weight 1 Opportunities Block KW2, Block KW4 Assessment The test consists of: * a written report, on an individual topic to be agreed upon with the lecturers; * an oral examination, based on the topic of the written report and on related content from the course. In addition to this, the students are required to complete three homework assignments throughout the semester. The final grade combines the scores from the written report (25%), oral examination (25%), and homework assignments (50%).