Groups and C*-Algebras

Course 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.

Education

MSc Programme in Mathematics

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.

4 hours lectures, 2 hours exercises/discussion per week for 8 weeks.

Functional Analysis (FunkAn) and Introduction to Operator Algebras (IntroOpAlg)

ECTS
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
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

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