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.
- Category
- Hours
- Exam
- 25
- Lectures
- 32
- Preparation
- 133
- Theory exercises
- 16
- Total
- 206
As
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- Credit
- 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.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
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.
Course information
- Language
- English
- Course code
- NMAK16011U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 4
- Schedule
- B
- Course capacity
- No restrictions/ no limitations
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Chris Cave (10-4e737d747e394e6c81704b786c7f73397680396f76)
- Magdalena Elena Musat (5-737b79677a4673677a6e34717b346a71)
- Mikael Rørdam (6-7976796b68744774687b6f35727c356b72)
Lecturers
Christopher Anthony Cave