6 ECTS credits
150 h study time

Offer 1 with catalog number 4013287FNR for all students in the 2nd semester of odd academic years (e.g. 2013-2014) at a (F) Master - specialised level.

Semester
biennial: 2nd semester of an odd academic year (e.g. 2013-2014)
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Enrollment Requirements
Registration for "Banach and C*-algebras" is allowed if one has successfully accomplished "Functional Analysis".
Taught in
English
Partnership Agreement
Under interuniversity agreement for degree program
Faculty
Faculty of Sciences and Bioengineering Sciences
Department
Mathematics
Educational team
Kenny De Commer (course titular)
Activities and contact hours

30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content

Part 1: Basic notions from C*-algebra theory

1. Banach algebras
2. Commutative Gelfand-Neumark theorem and functional calculus
3. Positivity, the GNS representation and the non-commutative Gelfand-Neumark theorem

Part 2: Basic notions von Neumann algebra theory

1. The von Neumann-Murray classification of factors (centerless von Neumann algebras)

2. The main results of Tomita-Takesaki theory (non-commutative integration)

3. Group von Neumann algebras (interplay between group theory and von Neumann algebra theory)

Course material
Digital course material (Recommended) : C*-algebra's, K. De Commer
Additional info

Notes will be provided. Supplementary references will be given throughout the course.

Learning Outcomes

General competencies

The student is familiar with basic concepts from the theory of commutative and non-commutative C*-algebra's and their representations. S/he is able to state and prove definitions and theorems from the course notes correctly. S/he can comment on those writings orally, and is able to make connections independently. S/he can explain how operator algebraic notions are extensions of classical topological or measure theoretical concepts. S/he can answer questions requiring insight/open questions. S/he can in particular apply the functional calculus. S/he is able to solve exercises similar to those provided during the course and to write up the answers in a correct and clear way.

 

Grading

The final grade is composed based on the following categories:
Written Exam determines 60% of the final mark.
PRAC Presentation determines 40% of the final mark.

Within the Written Exam category, the following assignments need to be completed:

  • Written exam with a relative weight of 60 which comprises 60% of the final mark.

    Note: written exam on basic theory C* and von Neumann algebras

Within the PRAC Presentation category, the following assignments need to be completed:

  • Presentatie with a relative weight of 40 which comprises 40% of the final mark.

    Note: Presentation (1 hour) about a proposed subject from a list of subjects

Additional info regarding evaluation

Written examination (exercises) and oral presentation on topic of choice

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)