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

Synopsis

• 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