Isometries of polyhedral Hilbert geometries

Lemmens, Bas and Walsh, Cormac (2011) Isometries of polyhedral Hilbert geometries. Topology and Analysis, 3 (2). pp. 213-241. ISSN 1793-5253. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1142/S1793525311000520

Abstract

We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n ≥ 2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex for all n ≥ 2, and find that it has the collineation group as an index-two subgroup. The results confirm several conjectures of P. de la Harpe for the class of polyhedral Hilbert geometries.

Item Type: Article
Uncontrolled keywords: Hilbert metric; horofunction boundary; detour metric; isometry group; collineations; Busemann points
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions: Central Services
Depositing User: Bas Lemmens
Date Deposited: 18 Nov 2011 14:36
Last Modified: 10 Jan 2012 11:45
Resource URI: https://kar.kent.ac.uk/id/eprint/28446 (The current URI for this page, for reference purposes)
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