On the automorphism group of a cone
On the automorphism group of a cone
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关于圆锥的自同构群
DOI：
10.1016/0024-3795(78)90035-6
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发表时间：
1978
影响因子：
1.1
通讯作者：
J. G. Horne
中科院分区：
文献类型：
--
作者：
J. G. Horne
设V是实有限维向量空间，C是满锥集。在证券交易委员会。3我们证明了V的紧凸子集的自同构群在一致拓扑中是紧的，并将C的自同构群与紧凸截面的自同构群联系起来。本节以一个应用程序结束，该应用程序推广了适当的洛伦兹变换在光锥中具有特征向量的结果。在证券交易委员会。4我们将C的自同构群与其不可约分支的自同构群联系起来。在证券交易委员会。5我们证明了C的每个自同构紧群都有一个紧凸截口不变量。应用这一结果证明了：如果C是全多面体锥，则C的自同构群是多面体截面的(有限)自同构群与其维度等于FC的不可约分支个数的向量群的半直积。一个例子表明，对于更一般的锥体，不存在这样的结果。
LetVbe a real finite dimensional vector space, and letCbe a full cone inC. In Sec. 3 we show that the group of automorphisms of a compact convex subset ofVis compact in the uniform topology, and relate the group of automorphisms ofCto the group of automorphisms of a compact convex cross-section ofC. This section concludes with an application which generalizes the result that a proper Lorentz transformation has an eigenvector in the light cone. In Sec. 4 we relate the automorphism group ofCto that of its irreducible components. In Sec. 5 we show that every compact group of automorphisms ofCleaves a compact convex cross-section invariant. This result is applied to show that ifCis a full polyhedral cone, then the automorphism group ofCis the semidirect product of the (finite) automorphism group of a polytopal cross-section and a vector group whose dimension is equal to the number of irreducible components ofC. An example shows that no such result holds for more general cones.