Skip to main content
SpringerLink
Log in

Positive Semicharacters of Lie Semigroups

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

We study positive semicharacters of generating Lie subsemigroup \(S\) of a connected Lie group \(G\). These semicharacters are important for positive representations of \(S\) in Hilbert space and for completely monotonic functions in \(S\). We describe the tangent map for a positive semicharacter and then obtain a necessary and sufficient condition for nontriviality of the wedge \(S_1^*\) consisting of all bounded positive semicharacters of \(S\). In particular \(S_1^*\) is nontrivial for a solvable simply connected \(G\) and invariant \(S\) without nontrivial subgroups, but it is trivial for a semisimple \(G\).

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. Devinatz, A. and Nussbaum, A.E.: 1961, Real characters of certain semigroups with applica-tions, Duke Math. J., 28, 221-237.

    Google Scholar 

  2. Nussbaum, A.E.: 1955, The Hausdorff-Bernstein-Widder theorem for semigroups in locally compact abelian groups, Duke Math. J., 22, 573-582.

    Google Scholar 

  3. Berg, C. et al.: 1984,Harmonic Analysis on Semigroups, Springer, New York

    Google Scholar 

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

  5. Mirotin, A.R.: 1998, Positive Semicharacters of Lie Semigroups, Abstracts International Conference on Mathematics and Applications Dedicated to the 90th Anniversary of L. S. Pontryagin. Moskow.

  6. Neeb, K.H.: 1993, Invariant subsemigroups of Lie groups, Mem. Amer. Math. Soc., 104, N 499.

    Google Scholar 

  7. Rieffel, M.A.: 1965, A caracterization of commutative group algebras and measure algebras, Trans. Amer. Math. Soc., 116, 32-65.

    Google Scholar 

  8. Gichev, V.M.: 1989, Invariant orderings in solvable Lie groups, Sib. Mat. Zhurnal, 30, 57-69.

    Google Scholar 

  9. Bourbaki, N.: 1972, Groups et algebras de Lie,Chapitres2 et3,Paris,Hermann.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Gomel State University, Sovietskaya, 104, 246699, Gomel, Belarus E-mail

    A.R. Mirotin

Authors
  1. A.R. Mirotin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mirotin, A. Positive Semicharacters of Lie Semigroups. Positivity 3, 23–31 (1999). https://doi.org/10.1023/A:1009703125617

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009703125617

Search

Navigation