6 ECTS credits
150 u studietijd
Aanbieding 1 met studiegidsnummer 4013287FNR voor alle studenten in het 2e semester van een oneven academiejaar (bvb. 2013-2014) met een gespecialiseerd master niveau.
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.
De beoordeling bestaat uit volgende opdrachtcategorieën:
Examen Schriftelijk bepaalt 60% van het eindcijfer
WPO Presentatie bepaalt 40% van het eindcijfer
Binnen de categorie Examen Schriftelijk dient men volgende opdrachten af te werken:
Binnen de categorie WPO Presentatie dient men volgende opdrachten af te werken:
Written examination (exercises) and oral presentation on topic of choice
Deze aanbieding maakt deel uit van de volgende studieplannen:
Master in de wiskunde: fundamentele wiskunde