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# innerDerivation -- make the derivation defined by right Lie multiplication by a Lie element

- Usage:
    `d=innerDerivation(u)`
- Inputs:
  - u, an instance of the type LieElement,
- Outputs:
  - d, an instance of the type LieDerivation, the inner derivation defined by $x$ \ \to\ [$x$,$u$]

## Description

    i1 : L = lieAlgebra{a,b}

    o1 = L

    o1 : LieAlgebra

    i2 : d=innerDerivation a a b

    o2 = d

    o2 : LieDerivation

    i3 : describe d

    o3 = a =>  - (a a b a)
         b =>  - (b a b a)
         map => id_L
         sign => 0
         weight => {3, 0}
         source => L
         target => L

    i4 : a (a a b)

    o4 =  - (a a b a)

    o4 : L

    i5 : b (a a b)

    o5 =  - (b a b a)

    o5 : L

## See also

- lieDerivation -- make a graded derivation
- LieDerivation -- the class of all Lie algebra derivations

## Ways to use innerDerivation:

- `innerDerivation(LieElement)`

## For the programmer

The object innerDerivation is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc2.m2:1856:0.