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lieIdeal -- make a Lie ideal

Description

The input should be a list $g$ of Lie elements in a Lie algebra $L$ or a subspace $S$ of $L$. The program adds generators to the input list or the subspace to make the ideal invariant under the differential. In the case when the input is a list, these extra non-normalized generators may be seen using gens(I).

Synopsis

  • Usage:
    I=lieIdeal(g)
  • Inputs:
  • Outputs:
    • I, an instance of the type LieIdeal, the ideal generated by the list $g$
i1 : F = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
               Signs=>{1,1,1},LastWeightHomological=>true)

o1 = F

o1 : LieAlgebra
 
i2 : D = differentialLieAlgebra({0_F,a a,a b})

o2 = D

o2 : LieAlgebra
 
i3 : I = lieIdeal{a b,c}

o3 = I

o3 : FGLieIdeal
 
i4 : gens I

o4 = {(a b), c,  - (a a a), (a b)}

o4 : List

Synopsis

  • Usage:
    I=lieIdeal(S)
  • Inputs:
  • Outputs:
    • I, an instance of the type LieIdeal, the ideal generated by the subspace $S$
i5 : C = cycles D

o5 = C

o5 : LieSubAlgebra
 
i6 : basis(4,C)

o6 = {(a a b), (b b) + 4 (a c)}

o6 : List
 
i7 : I = lieIdeal C

o7 = I

o7 : LieIdeal
 
i8 : basis(4,I)

o8 = {(a a b), (a c), (b b)}

o8 : List

See also

Ways to use lieIdeal:

  • lieIdeal(LieSubSpace)
  • lieIdeal(List)

For the programmer

The object lieIdeal is a method function.

The source of this document is in GradedLieAlgebras/doc.m2:1108:0.