
Journal of Lie Theory 12 (2002), No. 2, 357368 Copyright Heldermann Verlag 2002 The Outer Automorphism Group of Normalizers of Maximal Tori in Connected Compact Lie Groups JeanFrançois Hämmerli Dept. of Mathematics, Faculty of Science, Okayama University, 31 Tsushimanaka, 7008530 Okayama, Japan 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 H^{1}(W; T). [ Fulltextpdf (224 KB)] 