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

2009

Literature

Below is a list of selected references for further reading and background information.

K-theory

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

Baum-Connes conjecture

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

Modular Theory

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

Quantum groups

  1. Kassel, Quantum Groups
  2. Kassel, Rosso & Turaev, Quantum groups and knot invariants
  3. Klimyk & Schmudgen, Quantum groups and their representations
  4. Timmermann, An invitation to quantum groups and duality
  5. Charley & Presley, Quantum groups

Subfactors

  1. Jones & Sunder, Introduction to subfactors