Symmetric cones, the Hilbert and Thompson metrics
Symmetric cones, the Hilbert and Thompson metrics
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对称锥体、希尔伯特和汤普森度量
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发表时间：
2012
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通讯作者：
Aurélien Bosché
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作者：
Aurélien Bosché
对称锥可以被赋予至少两个有趣的非黎曼度量：希尔伯特度量和汤普森度量。保持锥的线性映射对于这两个度量是等距的，这是微不足道的。奇怪的是，这些并不是唯一的等距线。我们在这里给出了一个完整的描述的等距群的希尔伯特和汤普森度量基本上使用的理论欧几里德约旦代数。这些结果已由L.莫尔纳然而，在本文中，我们不做任何假设的对称锥在审查（它可以是可约的，并包含例外的因素）。
Symmetric cones can be endowed with at least two interesting non Riemannian metrics: the Hilbert and the Thompson metrics. It is trivial that the linear maps preserving the cone are isometries for those two metrics. Oddly enough those are not the only isometries in general. We give here a full description of the isometry groups for both the Hilbert and the Thompson metrics using essentially the theory of euclidean Jordan algebras. Those results were already proved for the symmetric cone of complexe positive hermitian matrices by L. Moln{'a}r. In this paper however we do not make any assumption on the symmetric cone under scrutiny (it could be reducible and contain exceptional factors).