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Homogeneous C*-algebras whose spectra are tori

Part of: Selfadjoint operator algebras Fiber spaces and bundles

Published online by Cambridge University Press:  09 April 2009

Shaun Disney  and
Iain Raeburn
Shaun Disney
Affiliation:
School of Mathematics University of New South WalesP. O. Box 1 Kensington, N.S.W. 2033, Australia
Iain Raeburn
Affiliation:
School of Mathematics University of New South WalesP. O. Box 1 Kensington, N.S.W. 2033, Australia
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Abstract

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By a theorem of Fell and Tomiyama-Takesaki, an N-homogeneous C*-algebra with spectrum X has the form Γ(E) for some bundle E over X with fibre MN(C), and its isomorphism class is determined by that of E and its pull-backs f*E along homeomorphisms f of X. We describe the homogeneous C*-algebras with spectrum T2 or T3 by classifying the MN-bundles over Tk using elementary homotopy theory. We then use our results to determine the isomorphism classes of a variety of transformation group C*-algebras, twisted group C*-algebras and more general crossed products.

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 46L40: Automorphisms 55R15: Classification
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 1 , February 1985 , pp. 9 - 39
Copyright
Copyright © Australian Mathematical Society 1985

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