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?
$\begingroup$
$\endgroup$
4
-
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-ÁlvarezCommented Oct 23, 2010 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 SnyderCommented Oct 24, 2010 at 0:58
-
$\begingroup$ The GAP package Quagroup does computations with quantum groups. See gap-system.org/Packages/quagroup.html $\endgroup$– uunknownCommented Oct 24, 2010 at 11:28
-
$\begingroup$ @Mariano-Suarez-Alvarez, PWB basis = what? $\endgroup$– sleepless in beantownCommented Oct 25, 2010 at 22:15
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
2
I just found the link to the QuantumGroups Mathematica package by Scott Morrison mentioned by Noah:
answered Oct 25, 2010 at 20:46
-
$\begingroup$ This package just seems to deal with quantized enveloping algebras. Is there an equivalent version for quantized coordinate algebras? $\endgroup$ Commented Oct 26, 2010 at 17:53
-
$\begingroup$ @John McCarthy: I don't know. $\endgroup$ Commented Oct 26, 2010 at 18:24