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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

0 votes
1 answer
176 views

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 …
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2 votes
2 answers
846 views

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), …
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  • 85
3 votes
1 answer
407 views

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 …
Davis's user avatar
  • 85
2 votes
1 answer
200 views

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 …
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