NMAK15008U C*Topics: K-theory for C*-algebras
MSc programme in Mathematics
K-theory is one of the most important tools in the study of C*-algebras. It associates to a given C*-algebra A two abelian groups, called K_0(A) and K_1(A), in a functorial way. These groups contain much information about the structure of the individual C*-algebra and there exists a powerful machinery which allows a computation of the K-groups in many cases.
In this course we focus on methods to compute the K-groups for C*-algebras and illustrate those by numerous examples and applications. More precisely, we will cover the following topics:
Quick repetition of the functors K_0, K_1 and their basic properties
Order structure on the K_0-group and Elliott’s classification of AF-algebras
The 6-term exact sequence with an explicit description of the boundary maps
The Pimsner-Voiculescu exact sequence for the K-theory of crossed products
Knowledge: The student will obtain knowledge of the elements mentioned in the description of the content.
Skills: Calculate K-groups, use basic classification results
Competences: Extract information about C*-algebras from their K-groups; gain access to K-theoretic classification results and more advanced parts of the theory
Rørdam, Larsen and Laustsen – An introduction to K-theory for C*-algebras
- 7,5 ECTS
- Type of assessment
- Continuous assessmentPass/fail based on 3 compulsory handins during the course.
- All aids allowed
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
One internal examiner
30 minutes oral exam without preparation time, several internal examiners, pass/ fail.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
- Project work