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

3 votes
2 answers
234 views

Reconstructing a Lie group Banach representation from the Lie algebra rep. on analytic vectors

Dear all, I have some difficulties with the following assertion in the book of Kirillov. Let $G$ be a connected Lie group, and T a given (!) representation of G on a Banach space V. Let $V^\omega$ b …
Amin's user avatar
  • 399
3 votes
1 answer
462 views

How can one find generators of basic differential forms on homogeneous spaces?

Dear all, In short, my problem is that I would like to have a better control of the 1-forms on a homogeneous space. Contrary to the group case, the module of differential form is not trivialisable. …
Amin's user avatar
  • 399
2 votes

Lie Groups and Manifolds

Just to comment on the relation between S^2 and SO(3) : there is indeed, for symmetric spaces, a natural correspondence between them and Lie groups, which in particular gives the S^2-SO(3) pair. A s …
Amin's user avatar
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