invImageLie -- computes the dimension for the inverse image of a map or derivation

Synopsis

• Usage:

  bb=invImageLie(n,f,b)

  bb=invImageLie(n,d,f,b)

• Inputs:

  • n, an integer, the degree
  • d, an integer, the homological degree
  • b, a list,
  • f, an object of class MapLie, a map
  • f, an object of class DerLie, a derivation
• Outputs:

  • dim, an integer,

Description

i1 : L=lieAlgebra({x,y},{},genSigns=>1)

o1 = L

o1 : LieAlgebra

i2 : M=lieAlgebra({a,b},{},genSigns=>1)

o2 = M

o2 : LieAlgebra

i3 : f = mapLie(L,M,{[x],[]})

o3 = f

o3 : MapLie

i4 : d = derLie(f,{[x,x],[x,y]})

o4 = d

o4 : DerLie

i5 : invImageLie(3,f,{[x,y,x]})

o5 = 2

i6 : invImageLie(3,d,{[x,y,x]})

o6 = 3

i7 : length intersectionLie(3,{imageBasisLie(3,f),{[x,y,x]}})+length kernelBasisLie(3,f)

o7 = 2

See also

• mapLie -- constructing a Lie algebra homomorphism
• derLie -- constructing a graded derivation
• imageLie -- gives the dimensions of the image of a Lie homomorphism up to a specified degree
• kernelLie -- gives the dimensions of the kernel of a Lie homomorphism up to a specified degree
• divisorLie -- computes a basis for the divisor subspace
• invImageBasisLie -- computes a basis for the inverse image of a map or derivation