Geodesic
Nonabelian Cohomology of Compact Lie Groups
Journal of Lie theory, Tome 19 (2009) no. 2, pp. 231-236.

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

Given a Lie group $G$ with finitely many components and a compact Lie group $A$ which acts on $G$ by automorphisms, we prove that there always exists an $A$-invariant maximal compact subgroup $K$ of $G$, and that for every such $K$, the natural map $H^1(A,K)\rightarrow H^1(A,G)$ is bijective. This generalizes a classical result of Serre and a recent result of the first and third named authors of the current paper.
Classification : 20J06, 22E15, 57S15
Mots-clés : Nonabelian cohomology, compact Lie group, maximal compact subgroup 
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     author = {J. An and M. Liu and Z. Wang },
     title = {Nonabelian {Cohomology} of {Compact} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {231--236},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JLT_2009_19_2_JLT_2009_19_2_a2/}
}
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J. An; M. Liu; Z. Wang . Nonabelian Cohomology of Compact Lie Groups. Journal of Lie theory, Tome 19 (2009) no. 2, pp. 231-236. http://geodesic.mathdoc.fr/item/JLT_2009_19_2_JLT_2009_19_2_a2/