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

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 …
Qayum Khan's user avatar
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 …
Qayum Khan's user avatar
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 …
Qayum Khan's user avatar