Journal of Lie Theory

no. 2
Nonabelian Cohomology of Compact Lie Groups
Jinpeng An1; Ming Liu1; Zhengdong Wang1
1School of Mathematical Sciences, Beijing University, Beijing 100871, P. R. China
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

Jinpeng An  1 ; Ming Liu  1 ; Zhengdong Wang  1

1 School of Mathematical Sciences, Beijing University, Beijing 100871, P. R. China 
Jinpeng An; Ming Liu; Zhengdong 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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     year = {2009},
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