# map(LieAlgebra,LieAlgebra,List) -- make a Lie algebra homomorphism

## Description

The optional inputs given above are not relevant for Lie algebras. The generators of M are mapped to the Lie elements in the last argument homdefs. The output map f might not be well defined and not commute with the differentials. It can be checked whether this is true by using isWellDefined(ZZ,LieAlgebraMap).

 i1 : L1=lieAlgebra({a,b},Signs=>1,LastWeightHomological=>true, Weights=>{{1,0},{2,1}})/{a a} o1 = L1 o1 : LieAlgebra i2 : F2=lieAlgebra({a,b,c}, Weights=>{{1,0},{2,1},{5,2}},Signs=>1,LastWeightHomological=>true) o2 = F2 o2 : LieAlgebra i3 : D2=differentialLieAlgebra{0_F2,a a,a a a b} o3 = D2 o3 : LieAlgebra i4 : L2=D2/{a a a a b,a b a b + a c} o4 = L2 o4 : LieAlgebra i5 : use L1 i6 : f=map(L1,L2,{a,0_L1,a b b}) warning: the map might not be well defined, use isWellDefined o6 = f o6 : LieAlgebraMap i7 : isWellDefined(6,f) the map is well defined for all degrees the map commutes with the differential for all degrees o7 = true i8 : describe f o8 = a => a b => 0 c => (a b b) source => L2 target => L1 i9 : use L2 i10 : f c c o10 = 2 (a b b a b b) o10 : L1