Isometries of polyhedral Hilbert geometries

2009/04/21 by Bas Lemmens, Cormac Walsh, Lemmens, Bas +1 · 1 citation
Mathematics · #22F50 #53C60 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.0904.3306

openalex publication_date 2009/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, and find that it has the collineation group as an index-two subgroup. These results confirm, for the class of polyhedral Hilbert geometries, several conjectures posed by P. de la Harpe.

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