NMAK16011U  Groups and C*-Algebras

Volume 2016/2017
Education

MSc Programme in Mathematics

Content

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.

Learning Outcome

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.
Functional Analysis (FunkAn) and Introduction to Operator Algebras (IntroOpAlg)
4 hours lectures, 2 hours exercises/discussion per week for 8 weeks.
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Each 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.

  • Category
  • Hours
  • Lectures
  • 32
  • Preparation
  • 133
  • Exam
  • 25
  • Theory exercises
  • 16
  • Total
  • 206