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.
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, Tome 19 (2009) no. 2, pp. 231-236. http://geodesic.mathdoc.fr/item/JOLT_2009_19_2_a2/
@article{JOLT_2009_19_2_a2,
author = {Jinpeng An and Ming Liu and Zhengdong Wang},
title = {Nonabelian {Cohomology} of {Compact} {Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {231--236},
year = {2009},
volume = {19},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2009_19_2_a2/}
}
TY - JOUR
AU - Jinpeng An
AU - Ming Liu
AU - Zhengdong Wang
TI - Nonabelian Cohomology of Compact Lie Groups
JO - Journal of Lie Theory
PY - 2009
SP - 231
EP - 236
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2009_19_2_a2/
ID - JOLT_2009_19_2_a2
ER -
%0 Journal Article
%A Jinpeng An
%A Ming Liu
%A Zhengdong Wang
%T Nonabelian Cohomology of Compact Lie Groups
%J Journal of Lie Theory
%D 2009
%P 231-236
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2009_19_2_a2/
%F JOLT_2009_19_2_a2
