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GradedLieAlgebras :: mapLie

mapLie -- constructing a Lie algebra homomorphism

Synopsis

Description

The generators of M are mapped to the Lie elements in the last argument homdefs. It is checked by the program that f maps the relations in M to zero and commutes with the differential and that f preserves the weight and sign. The effect of mapLie(L,M) is that the "common" generators are mapped to themselves and the other generators are mapped to zero (cf map for rings). Two generators are "common" if they have the same name and the same weight and sign.

i1 : L1=lieAlgebra({a,b},genSigns=>1,diffl=>true,
         genWeights=>{{1,0},{2,1}})/{a a}

o1 = L1

o1 : LieAlgebra
i2 : L2=lieAlgebra({a,b,c},
         genWeights=>{{1,0},{2,1},{5,2}},genSigns=>1,diffl=>true)

o2 = L2

o2 : LieAlgebra
i3 : L2=diffLieAlgebra{L2.zz,a a,a a a b}/{a a a a b,a b a b + a c}

o3 = L2

o3 : LieAlgebra
i4 : useLie L1

o4 = L1

o4 : LieAlgebra
i5 : f=mapLie(L1,L2,{a,L1.zz,a b b})

o5 = f

o5 : MapLie
i6 : peekLie f

o6 = MapLie{a => a         }
            b => 0
            c => (a b b)
            sourceLie => L2
            targetLie => L1
i7 : useLie L2

o7 = L2

o7 : LieAlgebra
i8 : f c c

o8 = 2 (a b b a b b)

o8 : L1
i9 : peekLie mapLie(L1,L2)

o9 = MapLie{a => a         }
            b => b
            c => 0
            sourceLie => L2
            targetLie => L1

See also

Ways to use mapLie :