# Mathematica package for Lie algebra computations?

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!

• What Lie groups are you interested in? If you're working with classical Lie groups the above would be wasting a lot of energy. – Ryan Budney Feb 17 '14 at 20:49
• Thanks, Ryan. I am working with generalizations of the Heisenberg algebra - i.e. higher-dimensional algebras that contain various copies of the Heisenberg algebra as subalgebras. – Idempotent Feb 17 '14 at 21:59
• There is a software called "Lie", and several user packages for maple, reduce, mathematica and other CAS. – Dietrich Burde Feb 17 '14 at 22:27
• @idempotent: Though I'm skeptical about doing much in this direction with Mathematica, I'd suggest looking into the extensive computational work on Lie algebras done by Willem A. deGraaf (who has specialized in this work for many years): front.math.ucdavis.edu/… – Jim Humphreys Feb 19 '14 at 19:39
• @JimHumphreys Yes, I like in particular papers $7$ and $16$ in front.math.ucdavis.edu/… !! – Dietrich Burde Feb 20 '14 at 20:19