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# map(LieDerivation) -- get the map in the definition of a Lie derivation

- Function: map
- Usage:
    `f = map(d)`
- Inputs:
  - d, an instance of the type LieDerivation,
- Optional inputs:
  - Degree => ..., default value null,
  - DegreeLift => ..., default value null,
  - DegreeMap => ..., default value null,
- Outputs:
  - f, an instance of the type LieAlgebraMap,

## Description

The optional inputs given above are not relevant for Lie algebras. If $d$ is a derivation $M \ \to\ L$, then there is defined a Lie algebra map $f: M \ \to\ L$, which determines the $M$-module-structure on $L$, and this map is represented by map(d).

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

    o1 = L

    o1 : LieAlgebra

    i2 : M=lieAlgebra({a,b},Signs=>0,Weights=>{2,2})

    o2 = M

    o2 : LieAlgebra

    i3 : f = map(L,M,{x x,x y})

    o3 = f

    o3 : LieAlgebraMap

    i4 : d = lieDerivation(f,{2 x,-y})

    o4 = d

    o4 : LieDerivation

    i5 : describe d

    o5 = a => 2 x
         b =>  - y
         map => f
         sign => 1
         weight => {-1, 0}
         source => M
         target => L

    i6 : d a b

    o6 = 0

    o6 : L

## See also

- map(LieAlgebra,LieAlgebra,List) -- make a Lie algebra homomorphism
- map(LieAlgebra,LieAlgebra) -- make a natural Lie algebra homomorphism
- map(LieAlgebra) -- get the map of a minimal model
- lieDerivation -- make a graded derivation
- Homomorphisms and derivations

## Ways to use this method:

- map(LieDerivation) -- get the map in the definition of a Lie derivation

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc.m2:1017:0.