Topological properties of Ad-semisimple conjugacy classes in Lie groups

2006/08/11 by Jinpeng An, An, Jinpeng
Mathematics · #17B05 #22E15 #57S25 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:17B05 #msc:22E15 #msc:57S25

paper · pdf · doi:10.48550/arxiv.math/0608280

15 pages

arxiv created 2006/08/11 · openalex publication_date 2006/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that Ad-semisimple conjugacy classes in a connected Lie group G are closed embedded submanifolds of G. We also prove that if α:H→ G is a homomorphism of connected Lie groups such that the kernel of α is discrete in H, then for an Ad-semisimple conjugacy class C in G, every connected component of α^-1(C) is a conjugacy class in H. Corresponding results for adjoint orbits in real Lie algebras are also proved.

Citations

• Arithmetic Subgroups of Algebraic Groups

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