The composition of maps $g*d$ is a derivation $M\ \to\ N$, with the composition $g*f$ defining the module structure of $N$ over $M$, where $f: M\ \to\ L$ defines the module structure of $L$ over $M$.
i1 : L = lieAlgebra{a,b}
o1 = L
o1 : LieAlgebra
|
i2 : d = lieDerivation{a a b,b b a}
o2 = d
o2 : LieDerivation
|
i3 : describe d
o3 = a => - (a b a)
b => (b b a)
map => id_L
sign => 0
weight => {2, 0}
source => L
target => L
|
i4 : N = lieAlgebra{a1,b1}
o4 = N
o4 : LieAlgebra
|
i5 : g = map(N,L,{b1,a1})
o5 = g
o5 : LieAlgebraMap
|
i6 : h = g*d
o6 = h
o6 : LieDerivation
|
i7 : describe h
o7 = a => (b1 b1 a1)
b => - (a1 b1 a1)
map => g
sign => 0
weight => {2, 0}
source => L
target => N
|