In this reading group we want to discuss topics in operator algebras. We started with K-theory, in particular these lecture notes by Klaas Landsman, see also the exercises. If you want to join the group, contact one of the organisers. The reading group is organised by Martijn Caspers, Pieter Naaijkens and Maarten van Pruijssen.

The current topic is quantum groups.

## Schedule

The intended timeslot is on fridays at 13:30 (HG03.084), but depending on availability of the participants this is subject to change.

### 2010

**Thursday January 21, 13:00:**Hopf algebras (Jord)**Friday January 19, 13:00:**Braided monoidal categories (Tim)**Tuesday February 2, 13:00:**Hopf algebras / Quantum double (Jord / Sander)**Friday, February 5, 10:30 (HG01.029):**Quantum double (Martijn)**Friday, February 12: no seminar because of GQT Colloquium!****Friday, February 19, 13:15 (!!) (HG 03.084):**Poincare-Birkhoff-Witt basis (Bram)**Friday: February 26: no seminar****Thursday, March 4, 13:30 (!!) (HG 03.084):**Representations of quantum doubles (Pieter)**Friday, March 12, 13:30 (HG 03.084):**Representations of quantum doubles II (Pieter)**Friday, March 19, 13:30 (HG 03.084):**C* quantum groups (Martijn)**Friday, April 9, 13:00 (!!) (HG 03.084):**Chapter 1 of Jones/Sunder (Pieter)**Thursday, April 15, 13:30 (HG 03.084):**Finish chapter 1 of Jones/Sunder (Pieter)**Friday, April 23, 13:30 (HG 03.084):**Beginning Chapter 2 (Martijn)**Wednesday, April 28, 13:30 (HG03.082):**End Chapter 2, begin Ch. 3 (Hester/Shoumin)**Friday, May 7, 13:30 (HG03.84):**Chapter 3 (Tim)**Wednesday, May 19, 13:30 (HG03.82):**Sections 4.1 and 4.2 (Martijn)**Friday, May 28, 13:30 (HG03.84):**Section 4.3 (Tim)**Wednesday, June 2, 13:30 (HG01.57):**Finish chapter 4 (Pieter)**Friday, June 11, 13:30 (HG03.84):**Chapter 5 (Martijn)

### 2009

**Thursday April 2, 13:30 (HG01.057):**Ch. 1-3 (Martijn)**Wednesday April 8, 15:30 (HG03.084):**Cancelled**Thursday April 16:**Cancelled**Wednesday May 6, 15:30 (HG03.084):**Ch. 4-5 (Maarten)**Wednesday May 13, 15:30 (HG03.084):**Ch. 6 (Maarten)**Tuesday May 19, 15:30:**Swan's Theorem (Jord)**Wednesday May 27, 15:30 (HG03.084):**Ch. 7-8 (Pieter)**Tuesday June 2, 13:30 (HG03.082):**Index map (Martijn)**Wednesday June 10, 15:30 (HG03.084):**Baum-Connes conjecture (Pieter)**Monday June 22, 10:45:**Bott periodicity (Tim)**Tuesday September 8, 13:30 (HG03.082):**Tomita-Takesaki Modular Theory (Martijn)**Tuesday September 15, 13:30 (HG03.054):**Examples, commutation theorem for tensor products (Pieter)**Tuesday September 22, 13:30 (HG03.054):**Tomita-Takesaki for weights (Martijn)**Tuesday September 29, 13:30 (HG03.054):**Type classification and modular theory (Pieter)**Tuesday October 6, 13:30 (HG03.632):**Harmonic analysis (Tim)

## Literature

Below is a list of selected references for further reading and background information.### K-theory

- Klaas Landsman,
*K-Theory for C* algebras*(download) - B. Blackader,
*K-Theory for operator algebras*, Mathematical Sciences Research Institute Publications 5 - G. Cortiñnas,
*Algebraic v. topological K-theory: a friendly match*, (arXiv:0903.3983) - P. Ara, F. Perara, A. Toms,
*K-Theory for operator algebras. Classification of C$^*$-algebras*, (arXiv:0902.3381) - M. Rørdam, F. Larsen, N.J. Laustsen,
*An Introduction to K-Theory for C*-algebras*, London Mathematical Society Student Texts 49

### Baum-Connes conjecture

- P. Baum, A. Connes, N. Higson,
*Classifying space for proper actions and K-theory of group C*-algebras*, Contemp. Math.**167**, 1994. (fulltext) - D. Matsnev,
*On the Baum-Connes conjecture*. (fulltext)

### Modular Theory

- M. Takesaki,
*Theory of Operator Algebras II* - F. LLedo,
*Modular theory by example*(arXiv:0902.3381) - Kadison and Ringrose,
*Fundamentals of the theory of operator algebras, vol. II* - Bratteli and Robinson,
*Operator Algebras and Quantum Statistical Mechanics I*(see here)

### Quantum groups

- Kassel,
*Quantum Groups* - Kassel, Rosso & Turaev,
*Quantum groups and knot invariants* - Klimyk & Schmudgen,
*Quantum groups and their representations* - Timmermann,
*An invitation to quantum groups and duality* - Charley & Presley,
*Quantum groups*

### Subfactors

- Jones & Sunder,
*Introduction to subfactors*