quotient(LieIdeal,FGLieSubAlgebra) -- make the quotient of a Lie ideal by a finitely generated Lie subalgebra

Synopsis

Function: quotient
Usage:

T=quotient(I,S)
Inputs:
- I, an instance of the type LieIdeal,
- S, an instance of the type FGLieSubAlgebra,
Optional inputs:
- BasisElementLimit => ..., default value infinity,
- DegreeLimit => ..., default value {},
- MinimalGenerators => ..., default value true,
- PairLimit => ..., default value infinity,
- Strategy => ..., default value null,
Outputs:
- T, an instance of the type LieSubAlgebra, the Lie elements that multiply all of $S$ into $I$

Description

The optional inputs given above are not relevant for Lie algebras. A Lie element $x$ is in $T$ if $x$ multiplies all the generators of $S$ into $I$. However, $T$ is not in general finitely generated.

i1 : L=lieAlgebra{a,b,c}/{a a b-c c b,b b a-b b c}

o1 = L

o1 : LieAlgebra

i2 : I=lieIdeal{a}

o2 = I

o2 : FGLieIdeal

i3 : S=lieSubAlgebra{b,c}

o3 = S

o3 : FGLieSubAlgebra

i4 : K=quotient(I,S)

o4 = K

o4 : LieSubAlgebra

i5 : basis(2,K)

o5 = {(b a), (c a), (c b)}

o5 : List

Ways to use this method: