Universal C*-algebras and von Neumann algebras

Dozent: Prof. Dr. Moritz Weber

Lecture

Thursday, 14-16

The language of the course is English, by default, unless all participants speak German.

News

There is an MS Teams with no. 133868. Please request the link from Moritz Weber.

Content

In this lecture, which is a continuation of the lecture Functional Analysis 2b (Operator algebras), we will focus on examples of universal C*-algebras (such as the Toeplitz algebra, the Cuntz algebra and the irrational rotation algebra) before we give an introduction to von Neumann algebras (bicommutant theorem, factors, type classification etc).

Script

We will treat Chapters 6 and 7 of the following script:
ISem24 Lecture Notes
See also the references below.

How to obtain the credit points

In order to obtain the credit points for this course, you must actively take part in the exercise sessions
and pass the oral exams at the end of the term which are the basis for your grade.

References

Books on operator algebras/C*-algebras:

Bruce Blackadar, Operator algebras. Theory of C*-algebras and von Neumann algebras, 2006.
Kenneth Davidson, C*-algebras by example, 1996.
Jacques Dixmier, Les C*-algebres et leurs representations, 1969.
Richard V. Kadison and John R. Ringrose, Fundamentals of the Theory of Operator Algebras.
Volume I-IV, 1997.
Gerard Murphy, C*-algebras and operator theory, 1990.
Masamichi Takesaki, Theory of Operator Algebras I-III, 2002/2003

Books and lecture notes on von Neumann algebras:

Claire Anantharaman and Sorin Popa, An introduction to II₁ factors, preliminary version.
Script by Vaughan Jones, Berkeley, 2009.
Lecture Notes Von Neumann algebras and ergodic theory of group actions, IHP 2011.
Script by Jesse Petersen, Vanderbilt, 2013.
Script by Sven Raum, Münster, 2015/2016.
Lecture Notes Von Neumann Algebras, Subfactors, Knots and Braids, and Planar Algebras
by Roland Speicher, Saarbrücken, 2016.
Lecture Notes by Cyril Houdayer, Paris

Postal address

Saarland University
Department of Mathematics
Postfach 15 11 50
66041 Saarbrücken
Germany

Physical address

Saarland University
Campus building E 2 4
66123 Saarbrücken
Germany