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Continuous trace C*-algebras with given Dixmer-Douady class

Part of: Selfadjoint operator algebras Homology and cohomology theories

Published online by Cambridge University Press:  09 April 2009

Iain Raeburn  and
Joseph L. Taylor
Iain Raeburn
Affiliation:
School of Mathematics University of New South WalesPost Office Box 1 Kensington, NSW, 2033, Australia
Joseph L. Taylor
Affiliation:
(usual address of J. L. Taylor: Department of Mathematics, University of UtahSalt Lake City Utah 84112, U.S.A.)
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Abstract

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We give an explicit construction of a continuous trace C*algebra with prescribed Dixmier-Douady class, and with only finite-dimensional irreducible representations. These algebras often have non-trivial automorphisms, and we show how a recent description of the outer automorphism group of a stable continuous trace C*algebra follows easily from our main result. Since our motivation came from work on a new notion of central separable algebras, we explore the connections between this purely algebraic subject and C*a1gebras.

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 46L40: Automorphisms 55N05: Čech types

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 3 , June 1985 , pp. 394 - 407
Copyright
Copyright © Australian Mathematical Society 1985

References

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