I'm trying to learn how to do algebraic manipulations in Mathematica but not finding the help very helpful. I'm going to ask about a specific quantum group example related to a previous question of mine. For $SU_q(N)$, how would I use Mathematica to show that
$$ S(u^1_2)u^3_1 = q^{-1}u^3_1S(u^1_2). $$ I am, of course, assuming that such a thing can be done in Mathematica. If I am wrong in this assumption, could someone please direct me a package that can do this calculation? Gap, Magma?

| cite | improve this question | | | | |
  • 1
    $\begingroup$ It can be done, with a non trivial amount of work. I have only managed to do this in situations where there is a PBW basis available, though. I'll post here an example of how one can deal with the (simpler!) Weytl algebra later. $\endgroup$ – Mariano Suárez-Álvarez Oct 23 '10 at 21:18
  • $\begingroup$ Scott Morrison has written an excellent quantum groups package in mathematica. Contact him at Scott tqft net and he can tell you more. $\endgroup$ – Noah Snyder Oct 24 '10 at 0:58
  • $\begingroup$ The GAP package Quagroup does computations with quantum groups. See gap-system.org/Packages/quagroup.html $\endgroup$ – uunknown Oct 24 '10 at 11:28
  • $\begingroup$ @Mariano-Suarez-Alvarez, PWB basis = what? $\endgroup$ – sleepless in beantown Oct 25 '10 at 22:15

I just found the link to the QuantumGroups Mathematica package by Scott Morrison mentioned by Noah:


| cite | improve this answer | | | | |
  • $\begingroup$ This package just seems to deal with quantized enveloping algebras. Is there an equivalent version for quantized coordinate algebras? $\endgroup$ – John McCarthy Oct 26 '10 at 17:53
  • $\begingroup$ @John McCarthy: I don't know. $\endgroup$ – mathphysicist Oct 26 '10 at 18:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.