Dear Jan Draisma,
You remarked:
I understand that the category
IsMagmaRingModuloRelations
is not inherited to factor structures, of which I think the universal
enveloping algebra of a Lie algebra is an example. The URL for
finitely presented algebras seems to be under construction.
That is correct; thank you for noting the broken link, we will fix that.
You asked:
My question: is there nevertheless an analogue of
CoefficientsAndMagmaElements
for u.e.algebras (which should use the PBW-basis)?
The operation `ExtRepOfObj' will give you a list of monomials with
their coefficients. For example:
gap> L:= SimpleLieAlgebra("A",2,Rationals);; gap> u:= UniversalEnvelopingAlgebra( L );; gap> g:= GeneratorsOfAlgebraWithOne( u ); [ [(1)*x.1], [(1)*x.2], [(1)*x.3], [(1)*x.4], [(1)*x.5], [(1)*x.6], [(1)*x.7], [(1)*x.8] ] gap> elm:= g[5]*g[4]*g[3]; [(1)*x.1*x.4+(-1)*x.2*x.5+(1)*x.3*x.4*x.5+(-1)*x.3*x.6+(1)*x.8] gap> ExtRepOfObj( elm ); [ 0, [ [ 1, 1, 4, 1 ], 1, [ 2, 1, 5, 1 ], -1, [ 3, 1, 4, 1, 5, 1 ], 1, [ 3, 1, 6, 1 ], -1, [ 8, 1 ], 1 ] ]
I hope this helps.
Best wishes,
Willem de Graaf