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