I am interested in performing Lie algebra computations in Mathematica. I did a bit of searching and found several packages (LieART, KILLING, SuperLie, maybe more), and wondered if anyone would recommend one over another.

What I am picturing doing is telling Mathematica my bracket structure and then using it to compute the multiplication in the Lie group (using the Baker-Campbell-Hausdorff-Dynkin formula) and then getting the adjoint and coadjoint actions. Basically what it boils down to is that I have to compute lots of brackets, and it seems more efficient for Mathematica to be doing that than me...

Thanks in advance for any and all perspectives!