The composition of maps d*g is a derivation N->L, with the composition f*g defining the module structure of L over N, where f: M->L defines the module structure of L over M.
i1 : L = lieAlgebra{a,b} o1 = L o1 : LieAlgebra |
i2 : M = lieAlgebra{a,b,c} o2 = M o2 : LieAlgebra |
i3 : N = lieAlgebra{a1,b1} o3 = N o3 : LieAlgebra |
i4 : f = mapLie(L,M) o4 = f o4 : MapLie |
i5 : useLie M o5 = M o5 : LieAlgebra |
i6 : g = mapLie(M,N,{b,a}) o6 = g o6 : MapLie |
i7 : useLie L o7 = L o7 : LieAlgebra |
i8 : d = derLie(f,{a a b,b b a,a a b+b b a}) o8 = d o8 : DerLie |
i9 : peekLie d o9 = 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 |
i10 : peekLie(f*g) o10 = MapLie{a1 => b } b1 => a sourceLie => N targetLie => L |
i11 : h = d*g o11 = h o11 : DerLie |
i12 : peekLie h o12 = a1 => (b b a) b1 => - (a b a) maplie => MapLie{a1 => b } b1 => a sourceLie => N targetLie => L sign => 0 weight => {2, 0} sourceLie => N targetLie => L |