# ideal(LieAlgebra) -- get the relations in a Lie algebra

## Synopsis

• Function: ideal
• Usage:
x=ideal(L)
• Inputs:
• Outputs:
• x, a list, $x$ may also be of type LieIdeal

## Description

The output is either the list of generators of the ideal or the ideal itself of type LieIdeal.

 i1 : L=lieAlgebra{a,b}/{a a a b,b b b a} o1 = L o1 : LieAlgebra i2 : ideal L o2 = { - (a a b a), (b b b a)} o2 : List i3 : describe L o3 = generators => {a, b} Weights => {{1, 0}, {1, 0}} Signs => {0, 0} ideal => { - (a a b a), (b b b a)} ambient => LieAlgebra{...10...} diff => {} Field => QQ computedDegree => 0 i4 : F=lieAlgebra{a,b} o4 = F o4 : LieAlgebra i5 : f=map(L,F) o5 = f o5 : LieAlgebraMap i6 : J=kernel f o6 = J o6 : LieIdeal i7 : N=F/J o7 = N o7 : LieAlgebra i8 : ideal N o8 = J o8 : LieIdeal