实经典群上的有理曲线

Zijia Li, Ke Ye
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引用次数: 0

摘要

本文主要研究实经典群上的有理曲线。我们的贡献有三个方面:(i) 我们确定了实经典群上二次有理曲线的结构。因此,我们对 $\mathrm{U}_n$, $\mathrm{O}_n(\mathbb{R})$, $\mathrm{O}_{n-1,1}(\mathbb{R})$ 和 $\mathrm{O}_{n-2,2}(\mathbb{R})$ 上的二次有理曲线进行了完全分类。(ii) 我们证明了实经典群上有理曲线的分解定理,它可以看作是代数基本定理和部分分数分解的非交换广义化。(iii) 作为(i)和(ii)的应用,我们将 Kempe 的普遍性定理推广到同质空间上的有理曲线。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rational Curves on Real Classical Groups
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify quadratic rational curves on $\mathrm{U}_n$, $\mathrm{O}_n(\mathbb{R})$, $\mathrm{O}_{n-1,1}(\mathbb{R})$ and $\mathrm{O}_{n-2,2}(\mathbb{R})$. (ii) We prove a decomposition theorem for rational curves on real classical groups, which can be regarded as a non-commutative generalization of the fundamental theorem of algebra and partial fraction decomposition. (iii) As an application of (i) and (ii), we generalize Kempe's Universality Theorem to rational curves on homogeneous spaces.
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