Curve Selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

2005/06/09 by Jinpeng An, Zhengdong Wang, An, Jinpeng +1
Computer Science · Engineering · Mathematics · #14P15 #22E15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Numerical methods in inverse problems #math.AG #math.GR #msc:14P15 #msc:22E15

paper · pdf · doi:10.48550/arxiv.math/0506160

6 pages

openalex publication_date 2005/06/09 · arxiv created 2005/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group G, each connected component of the set E_n(G) of all elements of order n in G is a conjugacy class in G. In particular, all conjugacy classes of finite order in G are closed. Some properties of connected components of E_n(G) are also given.

Related

• On conjugacy classes in the Lie group E₈
• Topological properties of Ad-semisimple conjugacy classes in Lie groups
• From conjugacy classes in the Weyl group to semisimple conjugacy classes
• Conjugacy classes of derangements in finite groups of Lie type
• Distinguished conjugacy classes and elliptic Weyl group elements