Skip to main content
SpringerLink
Log in

The foliation of semigroups by congruence classes

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

LetS be an open subsemigroup of a Lie groupG with\(1 \in \bar S\). We shall show that for every congruence ℋ onS with closed congruence classes there exists an open neighborhoodU of1 inG and a foliation ofS ∩U whose leaves locally coincide with both the congruence classes of ℋ and the cosets of a normal analytic subgroup ofG which is uniquely determined by ℋ.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bourbaki, N.: Groupes et algèbres de Lie, Chap. I–VIII. Paris: Hermann. 1971–1975.

    Google Scholar 

  2. Carruth, J. H., Hildebrandt, J. A., Koch, R. J.: The Theory of Topological Semigroups, Vol. I and II. New York: Marcel Dekker. 1983 and 1986.

    Google Scholar 

  3. Hilgert, J., Hofmann, K. H., Lawson, J. D.: Lie Groups, Convex Cones, and Semigroups. Oxford: University Press. 1989.

    Google Scholar 

  4. Hofmann, K. H.: Topologische Halbgruppen mit dichter submonogener Unterhalbgruppe. Math. Z.74, 232–276 (1960).

    Google Scholar 

  5. Hofmann, K. H., Mostert, P. S.: Elements of Compact Semigroups. Columbus, Ohio: Merrill Books. 1966.

    Google Scholar 

  6. Keimel, K.: Eine Exponentialfunktion für kompakte abelsche Halbgruppen. Math. Z.97, 7–25 (1967).

    Google Scholar 

  7. Keimel, K.: Lokal kompakte Kegelhalbgruppen und deren Einbettung in topologische Vektorräume. Math. Z.99, 405–428 (1967).

    Google Scholar 

  8. Keimel, K.: A cross section theorem for compact abelian semigroups. Semigroup Forum1, 254–259 (1970).

    Google Scholar 

  9. Keimel, K.: Congruence relations on cone semigroups. Semigroup Forum2, 130–147 (1971).

    Google Scholar 

  10. Lawson, J. D., Madison, B.: Quotients ofk-semigroups. Semigroup Forum9, 1–18 (1974).

    Google Scholar 

Download references

Author information

Author notes

  1. W. A. F. Ruppert

    Present address: Institut für Mathematik, Universität für Bodenkultur, A-1180, Wien, Austria

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-6100, Darmstadt, Germany

    K. H. Hofmann & W. A. F. Ruppert

Authors
  1. K. H. Hofmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. A. F. Ruppert
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This author gratefully acknowledges the support he received from the Alexander von Humboldt Foundation during the preparation of this paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hofmann, K.H., Ruppert, W.A.F. The foliation of semigroups by congruence classes. Monatshefte für Mathematik 106, 179–204 (1988). https://doi.org/10.1007/BF01318680

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01318680

Keywords

Search

Navigation