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May 21, 2014 at 9:00 vote accept Benjamin
May 14, 2014 at 18:25 comment added Benjamin I am aware that all left invariant vector fields are killing. I have arrived at the equation $g([a,w], a+w) = 0$ $\forall a \in \mathfrak{su}(n)$ as a condition for the specific case I mentioned. Is this a special case of your equation above?
May 14, 2014 at 17:41 history answered Peter Michor CC BY-SA 3.0