Geodesic
The Outer Automorphism Group of Normalizers of Maximal Tori in Connected Compact Lie Groups
Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 357-368

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Let G be a connected compact Lie group, T a maximal torus of G, N = NG(T) its normalizer and W = N/T the Weyl group of G. We show that the outer automorphism group of N canonically decomposes as a semidirect product, where the normal subgroup is given by the cohomology group H1(W; T).
Classification : 22E15
Mots-clés : Lie group, extensions of automorphisms, normalizer, maximal torus, Weyl group 
J.-F. Hämmerli. The Outer Automorphism Group of Normalizers of Maximal Tori in Connected Compact Lie Groups. Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 357-368. http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a2/
@article{JOLT_2002_12_2_a2,
     author = {J.-F. H\"ammerli},
     title = {The {Outer} {Automorphism} {Group} of {Normalizers} of {Maximal} {Tori} in {Connected} {Compact} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {357--368},
     year = {2002},
     volume = {12},
     number = {2},
     zbl = {0994.22005},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a2/}
}
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