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GradedLieAlgebras :: inverse(LieDerivation,LieSubSpace)

inverse(LieDerivation,LieSubSpace) -- make the inverse image of a Lie subspace under a Lie derivation

Synopsis

Description

If $S$ is an instance of LieIdeal, then $I$ is of type LieSubAlgebra. Otherwise, $I$ is of type LieSubSpace.

i1 : F = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
         Signs=>{1,1,1},LastWeightHomological=>true)

o1 = F

o1 : LieAlgebra
i2 : D = differentialLieAlgebra({0_F,a a,a b})

o2 = D

o2 : LieAlgebra
i3 : d = differential D

o3 = d

o3 : LieDerivation
i4 : B = boundaries D

o4 = B

o4 : LieSubAlgebra
i5 : x = (a a b a c) + (a a a b c)

o5 = (a a b a c) + (a a a b c)

o5 : D
i6 : member(x,B)

o6 = true
i7 : S = inverse(d,lieIdeal{x})

o7 = S

o7 : LieSubAlgebra
i8 : weight x

o8 = {8, 3}

o8 : List
i9 : basis(8,4,S)

o9 = {(a a c c), (b b a c) + (b a b c)}

o9 : List
i10 : d\oo

o10 = {2 (a a b a c) + 2 (a a a b c), 2 (a a b a c) + 2 (a a a b c)}

o10 : List

See also