> < ^ Date: Thu, 10 Jul 2003 15:21:51 +0200 (CEST)
< ^ From: Willem de Graaf <degraaf@math.uu.nl >
< ^ Subject: Re: Restricted universal enveloping algebra

Ciao Mimmo,

You asked about restricted enveloping algebras. In fact, some time
ago I have written a small package containing a function for creating
these algebras. It is called `penvelope', and can be found on my
homepage, www.math.uu.nl/people/graaf/penv.html.

An example:

gap> RequirePackage("penvelope");
                  PEnvelope!            true
gap> L:= SimpleLieAlgebra("A",2,GF(3) );
<Lie algebra of dimension 8 over GF(3)>
gap> u:= PEnvelopingAlgebra( L );
PEnvAlgebra( <Lie algebra of dimension 8 over GF(3)> )
gap> g:= GeneratorsOfAlgebra(u);
[ (Z(3)^0)*1, (Z(3)^0)*x1, (Z(3)^0)*x2, (Z(3)^0)*x3, (Z(3)^0)*x4,
  (Z(3)^0)*x5, (Z(3)^0)*x6, (Z(3)^0)*x7, (Z(3)^0)*x8 ]
gap> g[3]^3;
gap> g[8]^3;
gap> g[8]^4*g[5]^2*g[2];

If you have questions about it, please ask.

All the best,


Miles-Receive-Header: reply

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