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How to do Lie Algebras in Mathematica...

• To: mathgroup at smc.vnet.net
• Subject: [mg20751] How to do Lie Algebras in Mathematica...
• From: Melih Sener <melih at ks.uiuc.edu>
• Date: Wed, 10 Nov 1999 00:17:57 -0500
• Organization: TBG/Beckman Institute
• Sender: owner-wri-mathgroup at wolfram.com

Hi...

Lets say I want to generate the Lie Algebra [of say su(3)]
on Mathematica without going to explicitly 
constucting matrices for the generators...

So I want Mathematica to "learn" relations like:

[G_ij , G_kl] = (something)*G_mn

and I want to define a "commutator product" [A , B]
which is distributive, linear etc.

So that I can produce expressions for things like
[a*G_12+b*G_23, c*G_33+d*G_13] in an easy way...
[ "Distribute" is useful... but I don't know how to 
make mathematica learn to factor coefficents of generators
outside the commutator...]

What is the best way to do this?

Thanks,

Melih

• Follow-Ups:
  • Re: How to do Lie Algebras in Mathematica...
    • From: Daniel Lichtblau <danl@wolfram.com>