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Semigroups in the simply connected covering of SL(2)

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Abstract

Based on the parametrization proposed in [HH85], K.-H. Neeb investigated in [Ne91] the globality of a certain one-parameter family of Lorentzian cones in the universal covering group\(\widetilde{Sl}(2)\) of SI(2). In this article, we use the Pontrjagin Maximum Principle in order to obtain an explicit description of the semigroups generated by these cones, resp., to find conal curves which return to the identity. Furthermore we improve the description of the exponential function of\(\widetilde{Sl}(2)\).

An adequate general framework should be that of J. Hilgert in [Hi92] who investigated the globality resp. controllability of pointed generating conesC which are invariant under the adjoint action of a compact subgroupK that comes from an Iwasawa decompositionG=NAK.

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References

  • [HH85] Hofmann, K.H., and J. Hilgert,Old and New on Sl(2), Manuscripta Math.54 (1985), 17–52.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstraße 7, 6100, Darmstadt, Germany

    Dirk Mittenhuber

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  1. Dirk Mittenhuber
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Communicated by K. H. Hofmann

supported by a DFG-grant

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Mittenhuber, D. Semigroups in the simply connected covering of SL(2). Semigroup Forum 46, 379–387 (1993). https://doi.org/10.1007/BF02573580

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  • DOI: https://doi.org/10.1007/BF02573580

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