Dear Gap-forum, and Willem,

> Dear Jan,
>
> Thank you for your question. You asked:
>
> I'd like to work with finite-dimensional subspaces of a universal
> enveloping algebra
>
> This is possible in GAP. However, one needs to install some NiceVector
> machinery. The code below does that. If you read it into GAP, then
> it should be possible to work with finite-dimensional vector
> spaces of elements of a universal enveloping algebra.
Thank you; it works very nicely, even for a Weyl algebra that I
constructed by slightly changing your code for Universal Enveloping
algebras: if L is the Lie algebra with basis x_1,...,x_n,
D_1,..,D_n and One, the only non-zero brackets being
[x_i,D_i]=-One
Then the Weyl algebra is U(L)/(1-One). Hence, by changing the reduction
to normal form in UniversalEnvelopingAlgebra such that it simply
leaves out the power of One, one gets an easy implementation of the
Weyl algebra. The code you sent me `turns out' to work automatically for
this case, too (I realize that such reasoning is only o.k.
for doing some calculations, not for development purposes.)

Will the code you sent me be included in the next release? And also for
polynomial algebras?

Best regards,

Jan