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Re: How to do Lie Algebras in Mathematica...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20772] Re: [mg20751] How to do Lie Algebras in Mathematica...
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Thu, 11 Nov 1999 00:22:47 -0500
  • References: <199911100517.AAA19751@smc.vnet.net.>
  • Sender: owner-wri-mathgroup at wolfram.com

Melih Sener wrote:
> 
> 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

Here is a URL to a related mathgroup note I posted last April.

http://library.wolfram.com/mathgroup/archives/1999/Apr/msg00029.html

You'll want to modify the commutator I used to suite your needs.

If the methods in that note do not adequately address your needs let me
know and I can think it over some more.


Daniel Lichtblau
Wolfram Research


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