[GAP Forum] LieExteriorSquare -- HAP 1.9
Primoz Moravec
primoz.moravec at fmf.uni-lj.si
Sun Jun 27 17:39:28 BST 2010
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.
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