On the Picard group of a continuous trace -algebra

Author:
Iain Raeburn

Journal:
Trans. Amer. Math. Soc. **263** (1981), 183-205

MSC:
Primary 46M20; Secondary 18F25, 46L05, 58G12

MathSciNet review:
590419

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Abstract: Let be a continuous trace -algebra with paracompact spectrum , and let be the algebra of bounded continuous functions on , so that acts on in a natural way. An bimodule is an imprimitivity bimodule if it is an imprimitivity bimodule in the sense of Rieffel and the induced actions of on the left and right of agree. We denote by the group of isomorphism classes of imprimitivity bimodules under . Our main theorem asserts that . This result is well known to algebraists if is an -homogeneous -algebra with identity, and if is separable it can be deduced from two recent descriptions of the automorphism group due to Brown, Green and Rieffel on the one hand and Phillips and Raeburn on the other. Our main motivation was to provide a direct link between these two characterisations of .

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DOI:
https://doi.org/10.1090/S0002-9947-1981-0590419-3

Article copyright:
© Copyright 1981
American Mathematical Society