LieSubSpace -- the class of all Lie subspaces

Description

This type represents Lie subspaces, and has the subtypes LieIdeal, FGLieIdeal, LieSubAlgebra, FGLieSubAlgebra. A Lie subspace need not be invariant under the differential.

i1 : L = lieAlgebra{a,b}

o1 = L

o1 : LieAlgebra

i2 : S=lieSubSpace{a b}

o2 = S

o2 : LieSubSpace

i3 : I=lieIdeal{a b}

o3 = I

o3 : FGLieIdeal

i4 : instance(S,LieSubAlgebra)

o4 = false

i5 : dims(1,3,S)

o5 = {0, 1, 0}

o5 : List

i6 : dims(1,3,I)

o6 = {0, 1, 2}

o6 : List

Types of LieSubSpace:

LieSubAlgebra -- the class of all Lie subalgebras

Methods that use an object of class LieSubSpace:

generators(LieSubSpace) -- get the generators
image(LieAlgebraMap,LieSubSpace) -- make the image of a Lie subspace under a Lie algebra map
image(LieDerivation,LieSubSpace) -- make the image of a Lie subspace under a Lie derivation
inverse(LieAlgebraMap,LieSubSpace) -- make the inverse image of a Lie subspace under a Lie algebra map
inverse(LieDerivation,LieSubSpace) -- make the inverse image of a Lie subspace under a Lie derivation
isMember(LieElement,LieSubSpace) -- whether a Lie element belongs to a Lie subspace
lieIdeal(LieSubSpace) -- see lieIdeal -- make a Lie ideal
LieSubSpace + LieSubSpace -- make the sum of two Lie subspaces
LieSubSpace @ LieSubSpace -- make the intersection of two Lie subspaces
trace(ZZ,LieSubSpace,LieAlgebraMap) -- compute the trace of a Lie algebra map acting on a Lie subspace

For the programmer

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

The source of this document is in GradedLieAlgebras/doc.m2:352:0.

LieSubSpace -- the class of all Lie subspaces

Description

See also

Types of LieSubSpace:

Methods that use an object of class LieSubSpace:

For the programmer