ISOMETRIES OF POLYHEDRAL HILBERT GEOMETRIES
ISOMETRIES OF POLYHEDRAL HILBERT GEOMETRIES
复制标题
多面体希尔伯特几何的等距
DOI：
10.1142/s1793525311000520
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发表时间：
2009
影响因子：
0.8
通讯作者：
C. Walsh
中科院分区：
文献类型：
--
作者：
Bas Lemmens;C. Walsh
证明了多面体Hilbert几何的等距群与其共线(射影)群重合的充要条件是多面体不是n-≥为2的n-单形。此外，我们确定了n-单形上n-≥-2的Hilbert几何的等距群，并发现它的共线变换群是指数为2的子群。结果证实了P.de la Harpe关于多面体Hilbert几何的几个猜想。
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.