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Levi-Malcev decomposition

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108343] Levi-Malcev decomposition
  • From: Simon <simonjtyler at gmail.com>
  • Date: Sun, 14 Mar 2010 05:15:17 -0500 (EST)

Hi everyone,

I have a program that spits out a bunch of integer valued matrices
that generate a Lie algebra that I'm interested in.  I'd like to be
able to classify the algebras that I get - the first step of which is
(I think) performing a Levi-Malcev decomposition into solvable and
semisimple parts.  (eg http://en.wikipedia.org/wiki/Levi_decomposition).
The next part is then identifying the semisimple part (call it L) and
realizing the solvable part as a sum of L-modules.

So my question is - does anyone have some Mathematica code that can do
(any of) the above - and would you mind lending/giving it to me?

At the moment I turn the matrices into a form recognizable by GAP
(http://www.gap-system.org/).  I can get GAP to do the decomposition
and identify the complexification of the semisimple part. I would
rather avoid all the cut-and-pasting.  It's also nice having code that
you can play with (and yes I know that GAP is GPLv2).

The other option is to have my Mathematica program call GAP (there was
something similar done a while back:
http://www.gap-system.org/ForumArchive/Egner.1/Sebastia.1/%5BMathema.1/1.html)

--
Simon


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