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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!

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    $\begingroup$ What Lie groups are you interested in? If you're working with classical Lie groups the above would be wasting a lot of energy. $\endgroup$ Feb 17, 2014 at 20:49
  • $\begingroup$ 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. $\endgroup$
    – Idempotent
    Feb 17, 2014 at 21:59
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    $\begingroup$ There is a software called "Lie", and several user packages for maple, reduce, mathematica and other CAS. $\endgroup$ Feb 17, 2014 at 22:27
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    $\begingroup$ @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/… $\endgroup$ Feb 19, 2014 at 19:39
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    $\begingroup$ The links the previous comments are broken. Here's a link to Willem A. de Graaf's current webpage. $\endgroup$ Dec 9, 2020 at 16:34

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