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Positivity

, Volume 3, Issue 1, pp 23–31 | Cite as

Positive Semicharacters of Lie Semigroups

  • A.R. Mirotin
Article
  • 27 Downloads

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 \(G\).

Lie group Lie semigroup semicharacter completely monotonic function representation 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • A.R. Mirotin
    • 1
  1. 1.Department of MathematicsGomel State UniversityGomelBelarus E-mail

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