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

Cormac Walsh 1 
1 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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.
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https://hal.inria.fr/hal-00930929
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Submitted on : Tuesday, January 14, 2014 - 4:43:10 PM
Last modification on : Friday, July 8, 2022 - 10:04:15 AM

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Cormac Walsh. Gauge-reversing maps on cones, and Hilbert and Thompson isometries. Geometry and Topology, Mathematical Sciences Publishers, 2018, 22 (1), pp.55-104. ⟨10.2140/gt.2018.22.55⟩. ⟨hal-00930929⟩

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