LieAlgebraMap * LieDerivation -- composition of a homomorphism and a derivation

Synopsis

Usage:

h = g*d
Operator: *
Inputs:
- g, an instance of the type LieAlgebraMap, a homomorphism from L to N
- d, an instance of the type LieDerivation, a derivation from M to L
Outputs:
- h, an instance of the type LieDerivation, a derivation from M to N

Description

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 : 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