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Let $G$ and $H$ be compact Lie groups, Consider $Ext_{Lie}(G,H)$ the set of isomorphism of extensions of Lie groups: $$ 1\rightarrow G\rightarrow M\rightarrow H\rightarrow 1 $$ There exists a ...

Let $G$, $H$ be two compact Lie groups (possibly disconnected). Two short exact sequences of compact Lie groups $$ 0\rightarrow G\rightarrow M_1 \rightarrow H\rightarrow 0, $$ $$ 0\rightarrow G\...