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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

5 votes
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Which Lie algebra admit symplectic forms

Hello Amine, One of the most general facts is that, if a Lie group admits a torsion free and (locally) flat connection (some authors call it an affine structure) which is invariant under left tra …
Andre Diatta's user avatar
4 votes

Lie groups admitting flat (bi)invariant metrics.

If we are only interested in invariant metrics, I think the answer to your questions readily derives from J. Milnor's paper Milnor, J., Adv. Math. 21 (1976), no. 3, 293-329. Let G be a connected Li …
Andre Diatta's user avatar