About Killing Form

147 Views Asked by Bumbble Comm At 06 May 2026 - 4:22

How can I prove that why the Killing form for an abelian Lie algebra is $0$? Can you help with suggestions, references, answers?

thanks!

There are 1 best solutions below

Bumbble Comm On 12 Jan 2014 - 9:11 BEST ANSWER

Just use the definition. For abelian Lie algebra $[x,y]=0$ for any $x, y \in g $. So $ad_xy=0, \forall y \in g$...