
Journal of Lie Theory 18 (2008), No. 3, 541554 Copyright Heldermann Verlag 2008 Topological Properties of AdSemisimple Conjugacy Classes in Lie Groups Jinpeng An Dept. of Mathematics, ETH Zurich, Switzerland Current address: Dept. of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 anjinpeng@gmail.com We prove that every connected component of the zero locus in a connected Lie group G of any real polynomial without multiple roots is a conjugacy class. As applications, we prove that any Adsemisimple conjugacy class C of G is a closed embedded submanifold, and that for any connected subgroup H of G, every connected component of the intersection of C and H is a conjugacy class of H. Corresponding results for adjoint orbits in real Lie algebras are also proved. Keywords: Lie group, Lie algebra, conjugacy class, adjoint orbit. MSC: 22E15, 17B05, 57S25 [ Fulltextpdf (194 KB)] for subscribers only. 