NMAK16011U Groups and C*-Algebras
MSc Programme in Mathematics
Completely positive maps on C*-algebras and the Stinespring representation theorem, tensor products of Hilbert spaces and C*-algebras, nuclear C*-algebras, C*-algebras associated with discrete groups, amenable groups and properties of the group C*-algebras of amenable groups (e.g. nuclearity), free groups and their C*-algebras (including Powers' theorem about simplicity and uniqueness of trace), crossed products: construction, applications and examples.
After completing the course, the students will have:
Knowledge of the material mentioned in the description of the content.
Skills to read and understand research papers concerning topics discussed in lectures.
The following competences:
- Have a good overview and understanding of the interplay between C*-algebras and group theory.
- Master (at a satisfactory level) the fundamental results covered in the lectures, to the extent of understanding their proofs and be able to interconnect various results.
- 7,5 ECTS
- Type of assessment
- Continuous assessmentEach student will give a 2x45 min presentation of material (not covered in lectures) relevant to the topic of the course, coming either from a research paper or from the textbook itself.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
30 minutes oral examination with 30 min preparation time, during which all aids are allowed. Several internal examiners.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
- Theory exercises