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Representations of crossed products by coactions and principal bundles


Authors: M. B. Landstad, J. Phillips, I. Raeburn and C. E. Sutherland
Journal: Trans. Amer. Math. Soc. 299 (1987), 747-784
MSC: Primary 46L55; Secondary 22D25, 46M20
DOI: https://doi.org/10.1090/S0002-9947-1987-0869232-0
MathSciNet review: 869232
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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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DOI: https://doi.org/10.1090/S0002-9947-1987-0869232-0
Article copyright: © Copyright 1987 American Mathematical Society

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