image(LieAlgebraMap) -- make the image of a Lie algebra map

Synopsis

• Function: image

• Usage:

  I=image(f)

• Inputs:
  • f, an instance of the type LieAlgebraMap,
• Outputs:
  • I, an instance of the type FGLieSubAlgebra, the image of $f$, a finitely generated Lie subalgebra of the target of $f$

Description

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 : I=lieIdeal{b c - a c,a b,b r4 - a r4}

o3 = I

o3 : FGLieIdeal

i4 : Q=D/I

o4 = Q

o4 : LieAlgebra

i5 : f=map(Q,D)

o5 = f

o5 : LieAlgebraMap

i6 : T=image(f)

o6 = T

o6 : FGLieSubAlgebra

i7 : isSurjective f

o7 = true

See also

• image(LieAlgebraMap,LieSubSpace) -- make the image of a Lie subspace under a Lie algebra map
• image(LieDerivation,LieSubSpace) -- make the image of a Lie subspace under a Lie derivation
• image(LieDerivation) -- make the image of a Lie derivation
• kernel(LieAlgebraMap) -- make the kernel of a map
• inverse(LieAlgebraMap,LieSubSpace) -- make the inverse image of a Lie subspace under a Lie algebra map
• isSurjective(LieAlgebraMap) -- whether a Lie map is surjective