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THE GLIMM IDEAL SPACE OF A TWO-STEP NILPOTENT LOCALLY COMPACT GROUP

Published online by Cambridge University Press:  20 January 2009

Eberhard Kaniuth  and
William Moran
Eberhard Kaniuth
Affiliation:
Fachbereich Mathematik/Informatik, Universität Paderborn, D-33095 Paderborn, Germany ([email protected])
William Moran
Affiliation:
Department of Mathematics and Statistics, The Flinders University of South Australia, Adelaide 5001, Australia ([email protected])
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Abstract

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For a two-step nilpotent locally compact group $G$, we determine the Glimm ideal space of the group $C^*$-algebra $C^*(G)$ and its topology. This leads to necessary and sufficient conditions for $C^*(G)$ to be quasi-standard. Moreover, some results about the Glimm classes of points in the primitive ideal space $\mathrm{Prim}(C^*(G))$ are obtained.

AMS 2000 Mathematics subject classification: Primary 22D25. Secondary 22D10

Keywords

two-step nilpotent groupgroup $C^*$-algebraprimitive idealGlimm idealtopology on ideal spacesquasi-standard $C^*$-algebra
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 3 , October 2001 , pp. 505 - 526
Copyright
Copyright © Edinburgh Mathematical Society 2001