Journal of Lie Theory

no. 2
Nonabelian Cohomology of Compact Lie Groups
Journal of Lie Theory, Volume 19 (2009) no. 2, pp. 231-236
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.
DOI: 10.5802/jolt.549
Classification: 20J06, 22E15, 57S15
Keywords: Nonabelian cohomology, compact Lie group, maximal compact subgroup 
@article{JOLT_2009_19_2_a2,
     author = {J. An and M. Liu and Z. Wang},
     title = {Nonabelian {Cohomology} of {Compact} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {231--236},
     year = {2009},
     volume = {19},
     number = {2},
     doi = {10.5802/jolt.549},
     zbl = {1181.22012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.549/}
}
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%A M. Liu
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J. An; M. Liu; Z. Wang. Nonabelian Cohomology of Compact Lie Groups. Journal of Lie Theory, Volume 19 (2009) no. 2, pp. 231-236. doi: 10.5802/jolt.549

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