Valuation theory of indefinite orthogonal groups
Valuation theory of indefinite orthogonal groups
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DOI：
10.1016/j.jfa.2017.06.005
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发表时间：
2017-09-15
影响因子：
1.7
通讯作者：
Faifman, Dmitry
中科院分区：
文献类型：
--
作者：
Bernig, Andreas;Faifman, Dmitry
设SO+（p，q）表示带签名（p，q）的真实的正交群的单位连通分支.我们给出了一个完整的描述空间的连续和广义的平移和SO+（p，q）不变的估值，推广Hadwiger的分类欧氏等距不变的估值。由于独立的利益，我们确定的空间内的平移不变的估值类的Klain施耐德连续的估值，它严格包含所有连续的平移不变的估值。线性映射的拉回和推进操作自然地扩展到这个类。(C)2017爱思唯尔公司All rights reserved.
Let SO+(p, q) denote the identity connected component of the real orthogonal group with signature (p, q). We give a complete description of the spaces of continuous and generalized translation- and SO+(p, q) -invariant valuations, generalizing Hadwiger's classification of Euclidean isometry-invariant valuations. As a result of independent interest, we identify within the space of translation-invariant valuations the class of Klain Schneider continuous valuations, which strictly contains all continuous translation -invariant valuations. The operations of pull-back and push-forward by a linear map extend naturally to this class. (C) 2017 Elsevier Inc. All rights reserved.