map(LieAlgebra,LieAlgebra) -- make a natural Lie algebra homomorphism

Synopsis

Function: map
Usage:

f=map(L,M)
Inputs:
- L, an instance of the type LieAlgebra,
- M, an instance of the type LieAlgebra,
Optional inputs:
- Degree => ..., default value null,
- DegreeLift => ..., default value null,
- DegreeMap => ..., default value null,
Outputs:
- f, an instance of the type LieAlgebraMap, a map from $M$ to $L$

Description

The optional inputs given above are not relevant for Lie algebras. The effect of map(L,M) is that the "common" generators are mapped to themselves and the other generators are mapped to 0 (cf map for rings). Two generators are "common" if they have the same name and the same weight and sign. 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 : M = lieAlgebra{a,b,c}

o1 = M

o1 : LieAlgebra

i2 : L = lieAlgebra({a,b,d},Weights=>{2,1,1})

o2 = L

o2 : LieAlgebra

i3 : f = map(L,M)

o3 = f

o3 : LieAlgebraMap

i4 : describe f

o4 = a => 0
     b => b
     c => 0
     source => M
     target => L

Ways to use this method: