# 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:
• 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