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GradedLieAlgebras :: invImageLie

invImageLie -- computes the dimension for the inverse image of a map or derivation

Synopsis

Description

The list b should contain LieElement of the same weight. The output is the dimension for the inverse image under f of the space generated by b. This dimension for a MapLie f and a list b of elements of degree n may also be computed as the dimension of the intersection of imageBasisLie(n,f) and b plus the dimension of the kernel of f in degree n (or n - degLie(f) if f is a derivation).

i1 : L=lieAlgebra({x,y},genSigns=>1)

o1 = L

o1 : LieAlgebra
i2 : M=lieAlgebra({a,b},genSigns=>1)

o2 = M

o2 : LieAlgebra
i3 : f = mapLie(L,M,{x+y,x-y})

o3 = f

o3 : MapLie
i4 : d = derLie(f,{x x,x y})

o4 = d

o4 : DerLie
i5 : invImageLie(f,{x y x})

o5 = 1
i6 : invImageLie(d,{x y x})

o6 = 2
i7 : useLie L

o7 = L

o7 : LieAlgebra
i8 : length intersectionLie(3,{imageBasisLie(3,f),{x y x}})+length kernelBasisLie(3,f)

o8 = 1
i9 : length intersectionLie(3,{imageBasisLie(3,d),{x y x}})+length kernelBasisLie(2,d)

o9 = 2

See also

Ways to use invImageLie :