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Full Description
The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C$^*$-algebras. They make contributions to the study of C$^*$-envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.
Contents
Introduction
Preliminaries
Definitions and fundamental results
Maximal C$^*$-covers, iterated crossed products and Takai duality
Crossed products and the Dirichlet property
Crossed products and semisimplicity
The crossed product as the tensor algebra of a C$^*$-correspondence
Concluding remarks and open problems
Bibliography.
