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# LieSubAlgebra -- the class of all Lie subalgebras

## Description

This type represents Lie subalgebras (which are invariant under the differential), and has the subtypes LieIdeal, FGLieIdeal, FGLieSubAlgebra.

    i1 : L = lieAlgebra{a,b}

    o1 = L

    o1 : LieAlgebra

    i2 : S=lieSubAlgebra{a}

    o2 = S

    o2 : FGLieSubAlgebra

    i3 : I=lieIdeal{a}

    o3 = I

    o3 : FGLieIdeal

    i4 : instance(I,LieSubAlgebra)

    o4 = true

    i5 : instance(I,FGLieSubAlgebra)

    o5 = false

## See also

- LieIdeal -- the class of all Lie ideals
- FGLieSubAlgebra -- the class of all finitely generated Lie subalgebras

## Types of LieSubAlgebra:

- FGLieSubAlgebra -- the class of all finitely generated Lie subalgebras
- LieIdeal -- the class of all Lie ideals

## For the programmer

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc.m2:377:0.