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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

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