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Representations Of Crossed Products By Coactions And Principal Bundles, M B. Landstad, J Phillips, Iain Raeburn, C E. Sutherland

Faculty of Engineering and Information Sciences - Papers: Part A

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.