TOPOLOGICAL PROPERTIES OF Ad-SEMISIMPLE CONJUGACY CLASSES IN LIE GROUPS

  • JINPENG AN
  • Published 2006

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(C) is a conjugacy class in H. Corresponding results for adjoint orbits in real Lie algebras are also proved.

Cite this paper

@inproceedings{AN2006TOPOLOGICALPO, title={TOPOLOGICAL PROPERTIES OF Ad-SEMISIMPLE CONJUGACY CLASSES IN LIE GROUPS}, author={JINPENG AN}, year={2006} }