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GradedLieAlgebras :: generators(LieSubSpace)

generators(LieSubSpace) -- get the generators

Synopsis

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

See also