generators(LieSubSpace) -- get the generators

Synopsis

Function: generators
Usage:

g=generators(S)
Inputs:
- S, an instance of the type LieSubSpace, an instance of type LieSubSpace
Optional inputs:
- CoefficientRing => ..., default value null,
Outputs:
- g, a list, a list of generators for $S$ as a Lie ideal, or as a Lie subalgebra, or as a Lie subspace, or $g$ is undefined

Description

The optional input given above is not relevant for Lie algebras. Instead of generators one may use the abbreviation gens. If $S$ is of type FGLieIdeal, then the generators of $S$ are the generators of $S$ as an ideal. If $S$ is of type FGLieSubAlgebra, then the generators of $S$ are the generators of $S$ as a Lie subalgebra. If $S$ is of type LieSubSpace given by a finite set of generators, then the generators of $S$ are the generators of $S$ as a Lie subspace. In all other cases, if $S$ is of type LieSubSpace, then the function generators applied to $S$ is not defined.

i1 : F=lieAlgebra{a,b,c}

o1 = F

o1 : LieAlgebra

i2 : I=lieIdeal{a a b,a a c}

o2 = I

o2 : FGLieIdeal

i3 : L=F/I

o3 = L

o3 : LieAlgebra

i4 : gens I

o4 = { - (a b a),  - (a c a)}

o4 : List

i5 : J=kernel map(L,F)

o5 = J

o5 : LieIdeal

i6 : gens J
the subspace has no generators

Ways to use this method: