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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 …
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 …
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).
7
votes
Accepted
Locally compact + two-point homogeneous => Riemannian
Tits proves in [Tits, J. Sur certaines classes d'espaces homogènes de groupes de Lie, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8$^\circ$ 29 (1955), no. 3, 268 pp. MR0076286], page 220, the following.
I …