Representations of Crossed Products by Coactions and Principal Bundles
Open Access
- 1 February 1987
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 299 (2) , 747-784
- https://doi.org/10.2307/2000523
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.Keywords
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