Hostname: page-component-cb9f654ff-hn9fh Total loading time: 0 Render date: 2025-08-30T06:27:35.646Z Has data issue: false hasContentIssue false
  • English
  • Français

Kirillov Theory for a Class of Discrete Nilpotent Groups

Published online by Cambridge University Press:  20 November 2018

Haryono Tandra  and
William Moran
Haryono Tandra
Affiliation:
School of Pure Mathematics, The University of Adelaide, Adelaide, S.A. 5005, Australia e-mail: htandra@maths.adelaide.edu.au
William Moran
Affiliation:
Department of Electrical and Electronic Engineering, University of Melbourne, Victoria 3010, Australia e-mail: b.moran@ee.mu.oz.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is concerned with the Kirillov map for a class of torsion-free nilpotent groups $G$ . $G$ is assumed to be discrete, countable and $\pi $ -radicable, with $\pi $ containing the primes less than or equal to the nilpotence class of $G$ . In addition, it is assumed that all of the characters of $G$ have idempotent absolute value. Such groups are shown to be plentiful.

Keywords

22D10

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 4 , 01 August 2004 , pp. 883 - 896
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Baggett, L. W., Kaniuth, E. and Moran, W., Primitive ideal spaces, characters, and Kirillov theory for discrete nilpotent groups. J. Func. Anal. 150(1997), 175–203.Google Scholar
[2] Baumslag, G., Lecture Notes on Nilpotent Groups, Regional Conference Series in Mathematics, No. 2, American Mathematical Society, Providence, Rhode Island, 1971.Google Scholar
[3] Carey, A. L. and Moran, W., Characters of nilpotent groups. Math. Proc. Cambridge Philos. Soc. 96(1984), 123–137.Google Scholar
[4] Carey, A. L., Moran, W. and Pearce, C. E. M., A Kirillov theory for divisible nilpotent groups. Math. Ann. 301(1995), 119–133.Google Scholar
[5] Effros, E. G. and Hahn, F., Locally compact transformation groups and C*-algebras. Memoirs of the American Mathematical Society 75(1967).Google Scholar
[6] Fell, J. M. G., Weak containment and induced representations of groups II. Trans. Amer. Math. Soc. 110(1964), 424–447.Google Scholar
[7] Green, P., The local structure of twisted covariance algebras. Acta Math. 140(1978), 191–250.Google Scholar
[8] Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis. I. Springer-Verlag, Berlin/Heidelberg, 1963.Google Scholar
[9] Howe, R. E., On representations of discrete, finitely generated, torsion-free, nilpotent groups. Pacific J. Math. 73(1977), 281–305.Google Scholar
[10] Jacobson, N., Lie Algebras. Interscience Publishers, New York, 1962.Google Scholar
[11] Kirillov, A. A., Unitary representations of nilpotent Lie groups. Uspehi Mat. Nauk 17(1962), 57–110.Google Scholar
[12] Kurosh, A. G., The Theory of Groups. I. Chelsea, New York, 1960.Google Scholar
[13] Kurosh, A. G., The Theory of Groups. II. Chelsea, New York, 1960.Google Scholar
[14] Mal’cev, A. I., Nilpotent torsion-free groups. Izvestia Akad. Nauk SSSR Ser. Mat. 13(1949), 201–212. (Russian)Google Scholar
[15] Johnston, C. Pfeffer, Primitive ideal spaces of discrete rational nilpotent groups. Amer. J. Math. 117(1995), 323–325.Google Scholar
[16] Tandra, H. and Moran, W., Characters of the discrete Heisenberg group and of its completion. Math. Proc. Cambridge Philos. Soc. (To appear.)Google Scholar
[17] Thoma, E., Über unitäre Darstellungen abzählbarer, discreter Gruppen. Math. Ann. 153(1964), 111–138.Google Scholar
[18] Warfield, R. B., Nilpotent Groups, Lecture Notes in Mathematics 513, Springer-Verlag, Berlin, 1976.Google Scholar