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.
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)
Notes will be provided. Supplementary references will be given throughout the course.
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.
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:
Within the PRAC Presentation category, the following assignments need to be completed:
Written examination (exercises) and oral presentation on topic of choice
This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)