> < ^ Date: Fri, 30 May 2003 12:49:19 +0200 (CEST)
> < ^ From: Willem de Graaf <degraaf@math.uu.nl >
> < ^ Subject: Re: All subalgebras of the given algebra

Dear Ilya Yanok,

You asked:

How can I get all subalgebras (up to isomorphism) of given Lie algebra?

I don't know of any algorithm for that. It seems to be a very difficult
task. There certainly is no function in GAP that will do that.

How can I check if Lie algebra a is isomophic to another Lie algebra b?

This is rather difficult as well. If both Lie algebras are semisimple
then the solution is easy: just compute the root system of each
Lie algebra. In general it can be done by a Groebner basis computation.
This will work for small dimensional Lie algebras (it depends a bit on
the structure of the Lie algebras to which dimension one can get).
I have written some functions for that which are part of a small
package which you can download from


This contains an interface to the system Singular, which does the
Groebner basis computations. In order to use this you have to install
Singular, which you can get from


Furthermore, the operating system of your computer must be Unix,
otherwise the interface will not work.

All the best,

Willem de Graaf

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