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Journal of Lie Theory 18 (2008), No. 3, 541--554
Copyright Heldermann Verlag 2008

Topological Properties of Ad-Semisimple 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

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 Ad-semisimple 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

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