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GradedLieAlgebras :: LieSubSpace @ LieSubSpace

LieSubSpace @ LieSubSpace -- make the intersection of two Lie subspaces

Synopsis

Description

If both $A$ and $B$ are instances of LieIdeal, then $S$ is of tyoe LieIdeal. If both $A$ and $B$ are instances of LieSubAlgebra but not both of LieIdeal, then $S$ is of tyoe LieSubAlgebra. Otherwise, $S$ is of tyoe LieSubSpace.

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

o1 = L

o1 : LieAlgebra
i2 : A=lieIdeal{a}

o2 = A

o2 : FGLieIdeal
i3 : B=lieIdeal{b}

o3 = B

o3 : FGLieIdeal
i4 : S=A@B

o4 = S

o4 : LieIdeal
i5 : basis(3,S)

o5 = {(a b a), (b b a), (c b a), (b c a)}

o5 : List
i6 : T=A+B

o6 = T

o6 : FGLieIdeal
i7 : dims(1,3,L/T)

o7 = {1, 0, 0}

o7 : List
i8 : dims(1,5,L/A@B)

o8 = {3, 2, 4, 6, 12}

o8 : List
i9 : dims(1,5,L/A++L/B)

o9 = {4, 2, 4, 6, 12}

o9 : List

See also