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GradedLieAlgebras :: DerLie - DerLie

DerLie - DerLie -- Subtraction of Lie derivations

Synopsis

Description

The symbol - is used as infix notation for the subtraction of Lie derivations M->L with the same defining map f: M->L.

i1 : M = lieAlgebra{a,b}

o1 = M

o1 : LieAlgebra
i2 : L = lieAlgebra{a1,b1}

o2 = L

o2 : LieAlgebra
i3 : f = mapLie(L,M,{b1,a1})

o3 = f

o3 : MapLie
i4 : d = derLie(f,{a1,b1})

o4 = d

o4 : DerLie
i5 : e = derLie(f,{2 b1,2 a1})

o5 = e

o5 : DerLie
i6 : u = d-e

o6 = u

o6 : DerLie
i7 : peekLie u

o7 = a => a1 - 2 b1
     b =>  - 2 a1 + b1
     maplie => MapLie{a => b1       }
                      b => a1
                      sourceLie => M
                      targetLie => L
     sign => 0
     weight => {0, 0}
     sourceLie => M
     targetLie => L
i8 : u a b

o8 =  - 4 (b1 a1)

o8 : L