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GradedLieAlgebras :: inverse(LieAlgebraMap,LieSubSpace)

inverse(LieAlgebraMap,LieSubSpace) -- make the inverse image of a Lie subspace under a Lie algebra map

Synopsis

Description

If $S$ is an instance of LieIdeal, then $I$ is of type LieIdeal. If $S$ is an instance of LieSubAlgebra but not of LieIdeal, then $I$ is of type LieSubAlgebra. Otherwise, $I$ is of type LieSubSpace.

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

o1 = F

o1 : LieAlgebra
i2 : I=lieIdeal{b c - a c}

o2 = I

o2 : FGLieIdeal
i3 : Q=F/I

o3 = Q

o3 : LieAlgebra
i4 : f=map(Q,F)

o4 = f

o4 : LieAlgebraMap
i5 : J=lieIdeal{a b}

o5 = J

o5 : FGLieIdeal
i6 : K=inverse(f,J)

o6 = K

o6 : LieIdeal
i7 : dims(1,6,F/K)

o7 = {3, 1, 2, 3, 6, 9}

o7 : List
i8 : dims(1,6,Q/J)

o8 = {3, 1, 2, 3, 6, 9}

o8 : List

See also