Geodesic
Topological Properties of Ad-Semisimple Conjugacy Classes in Lie Groups
Journal of Lie theory, Tome 18 (2008) no. 3, pp. 541-554.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22E15, 17B05, 57S25
Mots-clés : Lie group, Lie algebra, conjugacy class, adjoint orbit 
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     author = {J. An },
     title = {Topological {Properties} of {Ad-Semisimple} {Conjugacy} {Classes} in {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {541--554},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a3/}
}
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J. An . Topological Properties of Ad-Semisimple Conjugacy Classes in Lie Groups. Journal of Lie theory, Tome 18 (2008) no. 3, pp. 541-554. http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a3/