60.10 Universal Enveloping Algebras

Returns the universal enveloping algebra of the Lie algebra L. The elements of this algebra are written on a Poincare-Birkhoff-Witt basis.

gap> L:= SimpleLieAlgebra( "A", 1, Rationals );;
gap> UL:= UniversalEnvelopingAlgebra( L );
<algebra-with-one of dimension infinity over Rationals>
gap> g:= GeneratorsOfAlgebraWithOne( UL );
[ [(1)*x.1], [(1)*x.2], [(1)*x.3] ]
gap> g[3]^2*g[2]^2*g[1]^2;
[(-4)*x.1*x.2*x.3^3+(1)*x.1^2*x.2^2*x.3^2+(2)*x.3^3+(2)*x.3^4]

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