NMAA13035U von Neumann Algebras (v.N.Alg)

Volume 2013/2014
Education
MSc Programme in Mathematics
Content

The course will cover the following subjects:
1) Desingy theorems for von Neumann algebras.
2) Comparison of projections
3) Type I, II and III von Neumann algebras
4) Finite and properly infinite von Neumann algebras
5) The trace on a finite factor
6) The von Neumann algebra associated to a discrete group
7) Examples of factors of Type III.

Learning Outcome
After completing the course the student will have the
Knowledge of the subjects mentioned in the description of the content.
Skills: The von Neumann algebra associated to a discrete group
Competences:
master the classical classification theory for von Neumann algebras. i.e. the type classification and the concept of finiteness. Moreover they should master the methods for constructing von Neumann algebras of type II from discrete groups and von Neumann algebras of type III group actions on measure spaces.
Introduction to Operator Algebras (IntroOpAlg).
4 hours of lectures and 3 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 1
  • Lectures
  • 28
  • Preparation
  • 156
  • Theory exercises
  • 21
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes with 30 minutes time for preparation
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
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.