# LieIdeal -- the class of all Lie ideals

## Description

This type represents Lie ideals. It is a subtype of LieSubAlgebra and it has FGLieIdeal as a subtype.

 i1 : L = lieAlgebra{a,b} o1 = L o1 : LieAlgebra i2 : I=lieIdeal{a a b} o2 = I o2 : FGLieIdeal i3 : Q=L/I o3 = Q o3 : LieAlgebra i4 : f=map(Q,L) o4 = f o4 : LieAlgebraMap i5 : J=kernel f o5 = J o5 : LieIdeal i6 : I===J o6 = false i7 : describe I o7 = generators => { - (a b a)} lieAlgebra => L

The kernel of $f$ is defined as the inverse image under $f$ of the zero ideal.

 i8 : describe J o8 = inverse => {f, finitely generated ideal of Q} lieAlgebra => L i9 : J#inverse_1===zeroIdeal Q o9 = true