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Results tagged with lie-groups
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user 47412
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
9
votes
Are maximal connected semisimple subgroups automatically closed?
If G is a simply connected Lie group and H a connected semisimple Lie subgroup then H is closed. Mostow Ann.Math. 1950, p. 615.
- 191
10
votes
Parallel forms and cohomology of symmetric spaces
As mentioned above, an invariant form on G/H is harmonic. The converse is proved in Helgason's book (1978), pages 227 and 564. The case of G itself is a theorem of Hodge.
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