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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
0
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1
answer
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Nilpotent subgroups of uniform finite index
Let $G$ be a Lie group, $K\subseteq G$ be a compact group and $N\subseteq$ be a nilpotent group s.t. $N\cap K= \{e\}$. Let $H=N\rtimes K$ be the semidirect product of $N$ and $K$ and let $\Gamma$ be a …
2
votes
2
answers
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Decomposing maximal compact subgroups of SO(n,1)
Let $G=SO(n,1)$ and let
$G=KAN$ be an Iwasawa decomposition of $G$. Let $M$ be the centralizer of $A$ in $K$. In this case, we have $K≃SO(n)$, $A≃\Bbb R$(this is the maximal diagonalizable subgroup), …
3
votes
1
answer
407
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Maximal nilpotent subgroups of SO(n,1)
For the Lie group $SO(n,1)$ I believe the maximal nilpotent subgroups are conjugate to either a diagonal group times a compact group or a unipotent group times a compact group. In either case the comp …
2
votes
1
answer
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Extending a discrete sub group to a lattice in unimodular Lie groups
Given a unimodular Lie group $G$ and a discrete subgroup $\Gamma\subseteq G$, under what conditions does there exists a discrete subgroup $H$ s.t. $\Gamma\subseteq H$ and $G/H$ has finite volume? Also …