Crossed products of C*-algebras by finite groups (Shanghai, July 2014)

This is the home page for N. C. Phillips' short course "Crossed products of C*-algebras by finite groups" at East China Normal University, Shanghai, 26--30 July 2014.

This course will be on crossed products of C*-algebras by actions of finite groups, with emphasis on the structure of the crossed product when the original algebra is simple and when the action satisfies sufficiently strong freeness conditions (such as the Rokhlin property or the tracial Rokhlin property). Some elementary knowledge of C*-algebras will be assumed, but group actions and crossed products will be defined and treated from scratch. The basics of crossed products by finite groups are particularly elementary, and provide an easy introduction to more general crossed products. To show how the theory fits together, I will sometimes mention what happens in more general situations, but without giving details.

Here are pdf files of a printable version of the lectures in Shanghai.

Lecture 1. A few misprints have been corrected. The file goes one slide beyond what I actually showed in that lecture.
Lecture 2 (corrected). Some misprints corrected, some additions and rearrangements, and additional exercises.
Lecture 3 (corrected). The slides include the more careful version of the proof at the end of the lecture, even though I didn't show that during the lecture.
Lecture 4 (corrected).
Lecture 5 (corrected). Changes: correction of misprints, and improvement of statements (especially towards the end).

Here are pdf files of a printable version of the slides for a series of three lectures on a very similar topic at the Research Institute for Mathematical Sciences, Kyoto University, in December 2011:

My draft notes on crossed product C*-algebras and minimal dynamics have a general discussion of crossed products by discrete groups, and several sections devoted to crossed products by actions of finite groups with the Rokhlin property or the tracial Rokhlin property. These notes are still very incomplete.

This page maintained by N. Christopher Phillips, email. Please email plain text (7 bit ASCII) only (no web page coded files, Microsoft Word documents, binary characters, etc.; see the email link for more).

Last significant change 12 July 2014.