The Outer Automorphism Group of Normalizers of Maximal Tori in Connected Compact Lie Groups

J.-F. Hämmerli

doi:10.5802/jolt.268

J.-F. Hämmerli

Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 357-368

Abstract

Let G be a connected compact Lie group, T a maximal torus of G, N = N_G(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).

EuDML Zbl

DOI: 10.5802/jolt.268

Classification: 22E15
Keywords: Lie group, extensions of automorphisms, normalizer, maximal torus, Weyl group

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     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},
     doi = {10.5802/jolt.268},
     zbl = {0994.22005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.268/}
}

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J.-F. Hämmerli. The Outer Automorphism Group of Normalizers of Maximal Tori in Connected Compact Lie Groups. Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 357-368. doi: 10.5802/jolt.268

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