# 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