Crossed products and the Mackey-Rieffel-Green machine

Abstract

We give an introduction into the ideal structure and representation theory of crossed products by actions of locally compact groups on C*-algebras. In particular, we discuss the Mackey-Rieffel-Green theory of induced representations of crossed products and groups. Although we do not give complete proofs of all results, we try at least to explain the main ideas. For a more detailed exposition of many of the results presented here we refer to the beautiful recent book by Dana Williams.

arXiv commentSome minor corrections of the previous version. The paper will appear as Chapter 2 of the book "K-theory for group C*-algebras and semigroup C*-algebras" which will appear in the Oberwolfach-seminar series of the Birkhäuser publishing company