Memoirs of the American Mathematical Society 1996; 134 pp; softcover Volume: 123 ISBN10: 0821805630 ISBN13: 9780821805633 List Price: US$48 Individual Members: US$28.80 Institutional Members: US$38.40 Order Code: MEMO/123/586
 The importance of separable continuous trace \(C^*\)algebras arises from the following facts: Firstly, their stable isomorphism classes are completely classifiable by topological data and, secondly, continuoustrace \(C^*\)algebras form the building blocks of the more general type I \(C^*\)algebras. This memoir presents an extensive study of strongly continuous actions of abelian locally compact groups on \(C^*\)algebras with continuous trace. Under some natural assumptions on the underlying system \((A,G,\alpha )\), necessary and sufficient conditions are given for the crossed product \(A{\times }_{\alpha }G\) to have continuous trace, and some relations between the topological data of \(A\) and \(A{\times }_{\alpha }G\) are obtained. The results are applied to investigate the structure of group \(C^*\)algebras of some twostep nilpotent groups and solvable Lie groups. For readers' convenience, expositions of the MackeyGreenRieffel machine of induced representations and the theory of Morita equivalent \(C^*\)dynamical systems are included. There is also an extensive elaboration of the representation theory of crossed products by actions of abelian groups on type I \(C^*\)algebras, resulting in a new description of actions leading to type I crossed products. Features:  The most recent results on the theory of crossed products with continuous trace.
 Applications to the representation theory of locally compact groups and structure of group \(C^*\)algebras.
 An exposition on the modern theory of induced representations.
 New results on type I crossed products.
Readership Graduate students and research mathematicians working in operator algebras or representation theory of locally compact groups. Theoretical physicists interested in operator algebras and \(C^*\)dynamical systems. Table of Contents  Abstract
 Introduction
 Preliminaries and basic definitions
 Morita equivalent twisted actions and duality
 Representations of type I abelian twisted systems
 Subgroup crossed products
 Crossed products with continuous trace
 Applications and examples
 Some concluding remarks
 References
