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4 votes
Accepted

Is the restriction of the Cartan 3-form on conjugacy classes exact?

Yes, it is exact, and there is in fact a canonical 2-form on each conjugacy class whose derivative is your $\Omega$. This was an important observation when studying D-branes in WZW models, see, e.g. ...
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1 vote
Accepted

Degenerate representation

Suppose $V = \mathbb{R}^n$ has a basis $(e_1,\dots,e_n)$. Your assumption is that you have a family of linear maps $\lambda_1,\dots,\lambda_m \in V^*$ which are defined such that $\lambda_r(e_i) = \...
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3 votes

Is every Lie subgroup of GL(V) isomorphic to a (maybe another) closed subgroup of GL(V)?

Just to flesh out Smilga's comment: The accepted answer is only valid for subgroups with finitely many connected components. For general subgroups the answer to OP is negative and an example is given ...
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