image(LieDerivation,LieSubSpace) -- make the image of a Lie subspace under a Lie derivation

Synopsis

Function: image
Usage:

I=image(d,S)
Inputs:
- d, an instance of the type LieDerivation,
- S, an instance of the type LieSubSpace, an instance of type LieSubSpace, a Lie subspace of the source of $d$
Outputs:
- I, an instance of the type LieSubSpace, an instance of LieSubSpace, the image $d(S)$, a Lie subspace of the target of $d$

Description

If $d$ is a differential on a Lie algebra $L$ and $S$ is an ideal in $L$, then image(d,S) is of type LieSubAlgebra. Otherwise, image(d,S) is of type LieSubSpace.

i1 : F=lieAlgebra({a,b,c,r3,r4,r42},
       Weights => {{1,0},{1,0},{2,0},{3,1},{4,1},{4,2}},Signs=>{0,0,0,1,1,0},
       LastWeightHomological=>true)

o1 = F

o1 : LieAlgebra

i2 : D=differentialLieAlgebra{0_F,0_F,0_F,a c,a a c,r4 - a r3}

o2 = D

o2 : LieAlgebra

i3 : S=lieIdeal{a r3}

o3 = S

o3 : FGLieIdeal

i4 : d=differential D

o4 = d

o4 : LieDerivation

i5 : T=image(d,S)

o5 = T

o5 : LieSubAlgebra

i6 : basis(5,T)

o6 = {(b a a c), (a a a c)}

o6 : List

Ways to use this method: