RingElement LieDerivation -- multiplication of a field element and a derivation

Synopsis

• Operator: SPACE

• Usage:

  e = a d

• Inputs:
  • a, a ring element, $a$ is an element in L#Field, where $L$ is the target of $d$
  • d, an instance of the type LieDerivation,
• Outputs:
  • e, an instance of the type LieDerivation,

Description

i1 : F = toField(ZZ/7[x]/{x^2+1})

o1 = F

o1 : PolynomialRing

i2 : M = lieAlgebra({a,b},Field=>F)

o2 = M

o2 : LieAlgebra

i3 : L = lieAlgebra({a,b},Field=>F)

o3 = L

o3 : LieAlgebra

i4 : f = map(L,M,{x a,3 b})

o4 = f

o4 : LieAlgebraMap

i5 : d = lieDerivation(f,{-x b,-2 a})

o5 = d

o5 : LieDerivation

i6 : describe (3*x) d

o6 = a => (3)b
     b => (x)a
     map => f
     sign => 0
     weight => {0, 0}
     source => M
     target => L

See also

• RingElement LieElement -- multiplication of a field element and a Lie element
• RingElement LieAlgebraMap -- multiplication of a field element and a homomorphism
• Number LieDerivation -- multiplication of a number and a derivation