MA8001 C*-crossed products (spring 2010)

This course gives an introduction to C*-crossed products. Among the things we will go through are the definitions and basic properties of the universal and the reduced crossed products of a locally compact group acting on a C*-algebra, and the Pimsner-Voiculescu exact sequence. The lectures will be given in turn by Magnus Landstad, Christian Skau and Toke Meier Carlsen. We also expect the participant to contribute (more on this later).

Time and place: Thursdays 13.15-15.00 in seminarrom 656, Sentralbygg II.

Literature

[B] Bruce Blackadar: K-theory for operator algebras, Second edition, Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. xx+300 pp. ISBN: 0-521-63532-2.

[T] Masamichi Takesaki: Theory of operator algebras. III, Encyclopaedia of Mathematical Sciences, 127. Operator Algebras and Non-commutative Geometry, 8. Springer-Verlag, Berlin, 2003. xxii+548 pp. ISBN: 3-540-42913-1.

[W] Dana P. Williams: Crossed Products of C*-algebras, Mathematical Surveys and Monographs, 134. American Mathematical Society, Providence, RI, 2007. xvi+528 pp. ISBN: 978-0-8218-4242-3; 0-8218-4242-0.

Schedule

Jan 28 Toke Meier Carlsen: C*-dynamical systems and covariant representations (2.1 up to and including Prop 2.7, and 2.2 up to and including Definition 2.10 [W]).
Feb 4 Toke Meier Carlsen: Covariant representations and the crossed product (the rest of 2.2 and 2.3 up to and including Prop. 2.23 of [W]).
Feb 10 Magnus Landstad: The crossed product (the rest of 2.3 of [W]).
Feb 18 Magnus Landstad: Representations of crossed products (all of 2.4 of [W] except 2.38 and 2.39).
Feb 25 Magnus Landstad: Takai duality (7.1 of [W]).
March 4 Magnus Landstad: Takai duality (7.1 of [W]).
March 11 Magnus Norling: The index map (8.3 of [B]).
March 17 Magnus Norling: The index map and Connes' Thom isomorphism (8.3, 10.2 and 10.9 of [B]).
March 24 Magnus Norling: Connes' Thom isomorphism (10.9 of [B]).
March 25 Magnus Norling: The Pimsner-Voiculescu exact sequence (10.3-10.4 of [B]).
April 14 Tron Omland: Amenable groups (Chapter XIII §4 of [T] and A2 of [W]).
April 22 Tron Omland: Amenable groups (Chapter XIII §4 of [T] and A2 of [W]).