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May 14, 2014 at 23:58 comment added José Figueroa-O'Farrill Yes, all I used was the ad-invariance of $b$.
May 14, 2014 at 23:27 comment added Benjamin Ok, thanks. That is really helpful. Am I right in thinking that the proof in your answer would be correct for arbitrary right invariant $b$ rather than just the killing form? I mean for a metric of the form in the original question but where $B$ is an arbitrary right invariant metric?
May 14, 2014 at 21:15 comment added José Figueroa-O'Farrill Sure, you can recover the general case by polarisation as usual.
May 14, 2014 at 19:11 comment added Benjamin Would it be sufficient to solve $(ad^*_z g)(x,x) = 0$ rather than introducing y also?
May 14, 2014 at 19:00 history answered José Figueroa-O'Farrill CC BY-SA 3.0