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