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Characters of nilpotent groups

Published online by Cambridge University Press:  24 October 2008

A. L Carey  and
W. Moran
A. L Carey
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT
W. Moran
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, SA
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Abstract

The characters (extremal positive definite central functions) of discrete nilpotent groups are studied. The relationship between the set of characters of G and the primitive ideals of the group C*-algebra C*(G) is investigated. It is shown that for a large class of nilpotent groups these objects are in 1–1 correspondence. One proof of this exploits the fact that faithful characters of certain nilpotent groups vanish off the finite conjugacy class subgroup. An example is given where the latter property fails.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 1 , July 1984 , pp. 123 - 137
Copyright
Copyright © Cambridge Philosophical Society 1984

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