1. ## Lie Bracket

If we have a f and g matrix, and n=2;

can we calculate ad_f^(n-4) g . Before this I just calculate for positive value like n-1. Thank you.

2. Originally Posted by ain
If we have a f and g matrix, and n=2;

can we calculate ad_f^(n-4) g . Before this I just calculate for positive value like n-1. Thank you.
I'm not quite sure what you're asking. Assuming this is $\text{ad}_{f^{n-4}}:\mathfrak{gl}_n\left(\mathbb{C}\right)\to \mathfrak{gl}_n\left(\mathbb{C}\right)$ (with the usual Lie bracket) then I see no way of simplifying your expression.