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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
10
votes
0
answers
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views
Is endoscopy interesting in simply-laced cases?
Let $G$ be a complex algebraic group, and write $Z(g)$ for the centralizer of a semisimple element $g$ in $G$. I will assume $G$ is simply connected, in which case $Z(g)$ is connected.
Let $G^\vee$ a …
60
votes
Homotopy groups of Lie groups
Here's another proof based on the structure of the flag variety $G/T$ of $G$. A compact Lie group $G$ has a maximal torus $T$, and $G$ is a principal $T$-bundle over the quotient $G/T$. Borel showed …