NMAA07012U Introduction to Operator Algebras (IntroOpAlg)
MSc Programme in Mathematics
Commutative Banach algebras, C*-algebras, commutative C*-algebras, continuous function calculus, states and representations, GNS representations, polar decomposition, non-unital C*-algebras and approximate units. AF algebras. Von Neumann algebras. The bicommutant theorem and Kaplansky's density theorem. Borel function calculus.
Knowledge:
The participants are expected to acquire the knowledge listed above
in the course description with an emphasis on
function calculus.
Skills:
The participants are expected to be able to understand and apply
the Gelfand transform and the GNS-construction, they must
understand basic facts about order. They must have some familiarity
with important examples of C*-algebras. They must understand the
basics of von Neumann algebras.
Competences:
The participants are expected to master the most fundamental
concepts and constructions for C*-algebras which are are used in
further studies in operator algebras and in non-commutative
geometry.
Kehe Zhu: An introduction to operator algebras (or equivalent), along with handout notes.
Academic qualifications equivalent to a BSc degree is recommended.
- Category
- Hours
- Exam
- 30
- Lectures
- 40
- Preparation
- 112
- Theory exercises
- 24
- Total
- 206
Individual written feedback on mandatory exercises. Individual or collective feedback on solutions presented by students at the exercise sessions.
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentThere will be given 3 assignments, each of which will count equally towards the final grade.
- 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.
Course information
- Language
- English
- Course code
- NMAA07012U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- A
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Søren Eilers (6-787c7f788586538074877b417e8841777e)