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GradedLieAlgebras :: imapLie

imapLie -- construction of a Lie map without checking correctness

Synopsis

Description

The construction is the same as for mapLie except that it is not checked that the relations are preserved and that the map commutes with the differential (and that the values of the generators preserve weight and sign). It is similar to the use of map for rings. E.g., it can be used to define a linear section of a map L->L/I. However, one has to be careful, since the map is declared to be an element in MapLie, which is wrong. The effect of imapLie(L,M) is the same as for mapLie(L,M), the "common" generators are mapped to themselves and the other generators are mapped to zero. Two generators are "common" if they have the same name and the same weight and sign.

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

o1 = L

o1 : LieAlgebra
i2 : M=lieAlgebra{a,b,c}

o2 = M

o2 : LieAlgebra
i3 : f = imapLie(L,M)

o3 = f

o3 : MapLie
i4 : s = imapLie(M,L)

o4 = s

o4 : MapLie
i5 : peekLie(f*s)

o5 = id

See also

Ways to use imapLie :