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Results tagged with lie-groups
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user 37911
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
4
votes
Accepted
Embedding flag manifolds of real semisimple lie group
If $P$ is any parabolic subgroup in a semisimple real Lie group $G$, one can
construct a $G$-equivariant embedding of the partial flag manifold $G/P$ into some (high dimensional) real projective space …
- 658
3
votes
Is every contractible homogeneous space of a connected Lie group homeomorphic to a Euclidean...
I don't have an answer. Note that $H$ need not be compact.
For example, $G$ could be the universal covering of $SL_2\mathbb R$, and
$H$ could be a $1$-dimensional closed subgroup.
Here are some more t …
- 658
6
votes
Conditions for a topological group to be a Lie group
Every locally compact and locally contractible topological group is a Lie group
(Hofmann-Neeb arXiv:math/0609684).
- 658
1
vote
Lie groups and NSS+LC group
Yes to both questions, assuming that the group $G$ is locally compact and
Hausdorff. In such a group one can always find an open subgroup $H$ which
is isomorphic to $(K\times L)/\Gamma$, where $K$ is …
- 658
12
votes
Accepted
spherical buildings for non-split groups
Misha, Tits' Lecture Note "Buildings of spherical type and finite BN pairs"
gives a fairly explicit description of the buildings associated to the
classical groups (not just the split ones). I also …
- 658