I have forwarded Mike Falk's question also to Arjeh Cohen at Eindhoven
who is'nt a member of the GAP-forum. He sent me the appended
interesting reply, which he allowed me to put into the GAP-forum. So
here is some further information about computing in Lie algebras with
GAP. Joachim Neubueser

======================================================================

Date: Thu, 24 Mar 1994 15:33:32 +0100
From: Arjeh Cohen <amc@win.tue.nl>

Dear Joachim,

Here is my answer to Mike Falk's query:

The kind of algorithms asked for are not in LiE,
BUT, as a start of the algorithms part of the ACELA
project, we are busy implementing the kind of algorithms
Mike Falk asked for.

We know how to implement the solvable radical of a subalgebra
of gl(n,k).
If the underlying field has characteristic 0, then it is already done
in GAP: we just compute the radical of the Killing form.
We are busy implementing the general algorithm in GAP as well,
this is more work.
Willem de Graaf, at Eindhoven, is working on it,
and expects to have it ready within a few weeks from now.

Thanks for keeping posting me the interesting GAP query.

Arjeh M. Cohen