[GAP Forum] LieExteriorSquare -- HAP 1.9

[Primoz Moravec]

Dear Forum,

I've been trying to use HAP 1.9 to work with the (non-abelian) Lie
exterior square of a Lie algebra. I define an algebra as follows:

T:=EmptySCTable(4,0,"antisymmetric");;
SetEntrySCTable(T,1,2,[1,3]);;
SetEntrySCTable(T,1,3,[1,4]);;
L:=LieAlgebraByStructureConstants(Rationals,T);;

Then I compute the exterior square of L. It is a record containing the
commutator map kappa : L\wedge L\to L, and the pairing p: L\times L\to L
\wedge L sending (x,y) to x\wedge y:

ext:=LieExteriorSquare(L);;
kappa:=ext.homomorphism;;
p:=ext.pairing;;

Now, I take two elements x and y of a basis of L, find the image
p(x,y)=x\wedge y in L\wedge L, and check whether this element belongs to
the source of kappa:

b:=Elements(Basis(L));;
p(b[3],b[4]) in Source(kappa);
false

I would appreciate if somebody told me what I've been doing wrong.

Primoz.