Nonabelian cohomology of compact Lie groups

Details Nonabelian cohomology of compact Lie groups Nonabelian cohomology of compact Lie groups

2009-04-19

arxiv.org/abs/0904.2903v1

Mathematics

Group Theory

7 pages

Scientific paper

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 $H^1(A,K)\to H^1(A,G)$ is bijective. This generalizes a classical
result of Serre [6] and a recent result in [1].

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