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 |
The object LieIdeal is a type, with ancestor classes LieSubAlgebra < LieSubSpace < VectorSpace < HashTable < Thing.