
Journal of Lie Theory 19 (2009), No. 2, 231236 Copyright Heldermann Verlag 2009 Nonabelian Cohomology of Compact Lie Groups Jinpeng An School of Mathematical Sciences, Beijing University, Beijing 100871, P. R. China anjinpeng@gmail.com Ming Liu School of Mathematical Sciences, Beijing University, Beijing 100871, P. R. China mingliulm@yahoo.com.cn Zhengdong Wang School of Mathematical Sciences, Beijing University, Beijing 100871, P. R. China zdwang@pku.edu.cn [Abstractpdf] 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. Keywords: Nonabelian cohomology, compact Lie group, maximal compact subgroup. MSC: 20J06, 22E15, 57S15 [ Fulltextpdf (152 KB)] for subscribers only. 