Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T14:00:05.590Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Alfsen, M.. Compact convex sets and boundary integrals. (Springer 1971).CrossRefGoogle Scholar
[2] Auslander, L. and Moore, C. C.. Unitary representations of solvable Lie groups. Mem. Amer. Math. Soc. 62 (1966).Google Scholar
[3] Chatard, J.. Applications des propriétés de moyenne d'un groupe localement compact à la théorie ergodique. Ann. Inst. H. Poincaré Sect. B (N.S.) 6 (1970), 307–326.Google Scholar
[4] Dixmier, J.. C *-algebras (North-Holland, 1977).Google Scholar
[5] Effros, E. Q.. Structure in simplexes. Acta Math. 117 (1967), 103–121.CrossRefGoogle Scholar
[6] Furstenberg, H.. Strict ergodicity and transformations of the torus. Amer. J. Math. 83 (1961), 573–601.CrossRefGoogle Scholar
[7] Green, P.. The local structure of twisted covariance algebras. Acta Math. 140 (1978), 191–250.CrossRefGoogle Scholar
[8] Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis. (Springer 1963).Google Scholar
[9] Howe, R. E.. On representations of discrete, finitely generated, torsion free, nilpotent groups. Pacific J. Math. 73 (1977), 281–305.CrossRefGoogle Scholar
[10] Kurosh, A. G.. The theory of groups, vol. II. (Chelsea 1956).Google Scholar
[11] Mal'cev, A. I.. On groups of finite rank. Mat. Sb. 22 (1948), 351–352.Google Scholar
[12] Moore, C. C. and Rosenberg, J.. Groups with T 1-primitive ideal spaces. J. Functional Anal. 22 (1976), 204–224.CrossRefGoogle Scholar
[13] Poguntke, G.. Discrete nilpotent groups have T 1 primitive ideal space. Studia Math. 71 (1981/1982), 271–275.CrossRefGoogle Scholar
[14] Pukanszky, L.. Characters of connected Lie groups. Acta Math. 133 (1974), 81–137.CrossRefGoogle Scholar
[15] Warfield, R. B.. Nilpotent Groups. Lecture Notes in Math. vol. 513. (Springer, 1976).CrossRefGoogle Scholar