Rational Curves on Real Classical Groups

2024/08/08 by Zijia Li, Ke Ye, Li, Zijia +1 · 1 citation
Mathematics · #14H45 #14L30 #14L35 #20G20 #26C15 #70B05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Symbolic Computation (cs.SC) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2408.04453

openalex publication_date 2024/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 U_n, O_n(ℝ), O_n-1,1(ℝ) and O_n-2,2(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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