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Representations of Crossed Products by Coactions and Principal Bundles

M. B. Landstad, J. Phillips, I. Raeburn and C. E. Sutherland
Transactions of the American Mathematical Society
Vol. 299, No. 2 (Feb., 1987), pp. 747-784
DOI: 10.2307/2000523
Stable URL: http://www.jstor.org/stable/2000523
Page Count: 38
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Representations of Crossed Products by Coactions and Principal Bundles
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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.

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