Journal of Lie Theory

no. 3
Topological Properties of Ad-Semisimple Conjugacy Classes in Lie Groups
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 541-554
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.
DOI: 10.5802/jolt.510
Classification: 22E15, 17B05, 57S25
Keywords: Lie group, Lie algebra, conjugacy class, adjoint orbit 
@article{JOLT_2008_18_3_a3,
     author = {J. An},
     title = {Topological {Properties} of {Ad-Semisimple} {Conjugacy} {Classes} in {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {541--554},
     year = {2008},
     volume = {18},
     number = {3},
     doi = {10.5802/jolt.510},
     zbl = {1162.22006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.510/}
}
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%A J. An
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J. An. Topological Properties of Ad-Semisimple Conjugacy Classes in Lie Groups. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 541-554. doi: 10.5802/jolt.510

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