Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Groups and C*-Algebras

Practical information
Study year 2016/2017
Block 4
Programme level Full Degree Master
Course responsibles
  • Chris Cave (10-486d776e783348667b6a457266796d33707a336970)
  • Magdalena Elena Musat (5-737b79677a4673677a6e34717b346a71)
  • Mikael Rørdam (6-7976796b68744774687b6f35727c356b72)
  • Department of Mathematical Sciences
Course number: NMAK16011U

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.

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.

Recommended prerequisites

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

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MSc Programme in Mathematics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


Christopher Anthony Cave


1 block


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Teaching and learning methods

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


No restrictions/ no limitations




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


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.


All aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

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

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.

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