New answers tagged lie-algebras
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. ...
- 3,789
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) = \...
- 2,642
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 ...
- 7,501
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