This Type represents derivations d from M to L, where M and L are Lie algebras. There is also a homomorphism f from M to L defining L as an M-module (f is the identity for the case of ordinary derivations from L to L). The derivation law reads
d[x,y]=[dx,fy]+/- [fx,dy]
where the sign is determined by the sign of interchanging d and x.
i1 : L = lieAlgebra{a,b} o1 = L o1 : LieAlgebra |
i2 : M = lieAlgebra{a,b,c} o2 = M o2 : LieAlgebra |
i3 : f = mapLie(L,M) o3 = f o3 : MapLie |
i4 : useLie L o4 = L o4 : LieAlgebra |
i5 : der = derLie(f,{a a b,b b a,a a b+b b a}) o5 = der o5 : DerLie |
i6 : peekLie der o6 = a => - (a b a) b => (b b a) c => - (a b a) + (b b a) maplie => MapLie{a => a } b => b c => 0 sourceLie => M targetLie => L sign => 0 weight => {2, 0} sourceLie => M targetLie => L |
i7 : useLie M o7 = M o7 : LieAlgebra |
i8 : der a c o8 = - (a a b a) + (b a b a) o8 : L |
The object DerLie is a type, with ancestor classes MutableHashTable < HashTable < Thing.