Representations of crossed products by coactions and principal bundles

Authors

M B. Landstad, University of Trondheim
J Phillips, University of Victoria
Iain Raeburn, University of WollongongFollow
C E. Sutherland, Mathematical Sciences Research Insitute

RIS ID

18825

Publication Details

Landstad, M. B., Phillips, J., Raeburn, I. & Sutherland, C. E. (1987). Representations of crossed products by coactions and principal bundles. Transactions of the American Mathematical Society, 299 (2), 747-784.

Abstract

The main purpose of this paper is to establish a covariant representation theory for coactions of locally compact groups on C^*-algebras (including a notion of exterior equivalence), to show how these results extend the usual notions for actions of groups on C^*-algebras, and to apply these ideas to classes of coactions termed pointwise unitary and locally unitary to obtain a complete realization of the isomorphism theory of locally trivial principal G-bundles in this context. We are also able to obtain all (Cartan) principal G-bundles in this context, but their isomorphism theory remains elusive.