Representations of crossed products by coactions and principal bundles

Landstad, M. B.; Phillips, J.; Raeburn, I.; Sutherland, C. E.

doi:10.1090/S0002-9947-1987-0869232-0

Representations of crossed products by coactions and principal bundles
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by M. B. Landstad, J. Phillips, I. Raeburn and C. E. Sutherland

Trans. Amer. Math. Soc. 299 (1987), 747-784

DOI: https://doi.org/10.1090/S0002-9947-1987-0869232-0

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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 ${C^{\ast }}$-algebras (including a notion of exterior equivalence), to show how these results extend the usual notions for actions of groups on ${C^{\ast }}$-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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