Gauge-reversing maps on cones, and Hilbert and Thompson isometries

Cormac Walsh 1, 2
1 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone.
Type de document :
Pré-publication, Document de travail
Preprint arXiv:1312.7871. 2013
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https://hal.inria.fr/hal-00930929
Contributeur : Cormac Walsh <>
Soumis le : mardi 14 janvier 2014 - 16:43:10
Dernière modification le : jeudi 10 mai 2018 - 02:05:59

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  • HAL Id : hal-00930929, version 1
  • ARXIV : 1312.7871

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Cormac Walsh. Gauge-reversing maps on cones, and Hilbert and Thompson isometries. Preprint arXiv:1312.7871. 2013. 〈hal-00930929〉

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