[GAP Forum] universal enveloping algebras

[Willem De Graaf]

Dear R.N. Tsai,

You asked

>   
>  If there's another way to map the generators of UL such that :
>  x -> x
>  d -> d
>  t -> 1 
>  so that [d,x]=1 and not [d,x]=t, then this would suffice for what I'm doing.
>I am running "GAP4, Version 4.4.6 of 02-Sep-2005, i686-pc-cygwin-gcc"
>  Thanks for you help.
>
>  
>
As far as I am aware, there is currently no way in GAP for doing this,
because there are no constructions of algebras with generators that satisfy
the ralations you indicate.
Also, I am not exactly sure what you want. There is no algebra homomorphism
that does the indicated thing: in the universal enveloping algebra we also
have the relation dt-td=-2d. So if you map t to 1 by an algebra 
homomorphism,
then you have to map d to 0.

All the best,

Willem de Graaf