This Type represents homomorphisms f from M to L, where M and L are Lie algebras. Use the constructor mapLie to define homomorphisms. A homomorphism is given by the value of the generators and it should preserve weight and sign. Observe that the zero element is considered to have any weight (and sign). The zero element in L is denoted L.zz.
i1 : M = lieAlgebra({a,b,c},genWeights=>{2,1,1}) o1 = M o1 : LieAlgebra |
i2 : L = lieAlgebra{a,b} o2 = L o2 : LieAlgebra |
i3 : f = mapLie(L,M,{a b,a,L.zz}) o3 = f o3 : MapLie |
i4 : peekLie f o4 = MapLie{a => - (b a) } b => a c => 0 sourceLie => M targetLie => L |
i5 : useLie M o5 = M o5 : LieAlgebra |
i6 : f (a c - a b) o6 = - (a b a) o6 : L |
The object MapLie is a type, with ancestor classes MutableHashTable < HashTable < Thing.