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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

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 …
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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 …
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  • 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).
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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 …
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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 …
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