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Results tagged with lie-groups
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user 16862
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
6
votes
1
answer
918
views
Uniform lattices in semisimple Lie groups
Let $\Gamma$ be a uniform lattice in a semisimple Lie group $G$.
Must $\Gamma$ be virtually torsion-free?
If (1) is true, then does this work more generally if $G$ is reductive?
I am motivated by …
- 687
1
vote
1
answer
303
views
Periodic automorphism of nilpotent Lie algebra
Are there a non-abelian nilpotent Lie algebra $\mathfrak{n}$ over $\mathbb{R}$ and an automorphism $\alpha: \mathfrak{n} \to \mathfrak{n}$ such that:
$\alpha$ is periodic,
the fixed subspace of $\al …
- 687
1
vote
Countability of conjugacy classes of closed subgroups
The countability of the number of conjugacy classes of closed subgroups of any compact Lie group is, in fact, a simple corollary of ideas that predate the end of World War II. Unfortunately, the earl …
- 687