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. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
