kernel(LieAlgebraMap) -- make the kernel of a map

Synopsis

• Function: kernel

• Usage:

  I=kernel(f)

• Inputs:
  • f, an instance of the type LieAlgebraMap
• Optional inputs:
  • SubringLimit => ..., default value infinity,
• Outputs:
  • I, an instance of the type LieIdeal, the kernel of $f$

Description

i1 : L = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
            Signs=>{1,1,1},LastWeightHomological=>true)

o1 = L

o1 : LieAlgebra

i2 : D= differentialLieAlgebra({0_L,a a,a b})

o2 = D

o2 : LieAlgebra

i3 : Q=D/{b b+4 a c}

o3 = Q

o3 : LieAlgebra

i4 : R=Q/{a b b}

o4 = R

o4 : LieAlgebra

i5 : f=map(R,Q)

o5 = f

o5 : LieAlgebraMap

i6 : I=kernel f

o6 = I

o6 : LieIdeal

i7 : basis(6,I)

o7 = {(a a a a b), (a a a c)}

o7 : List

See also

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