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GradedLieAlgebras :: DerLie * MapLie

DerLie * MapLie -- operation of maps to the right of a derivation

Synopsis

Description

The composition of maps d*g is a derivation N->L, with the composition f*g defining the module structure of L over N, where f: M->L defines the module structure of L over M.

i1 : L = lieAlgebra{a,b}

o1 = L

o1 : LieAlgebra
i2 : M = lieAlgebra{a,b,c}

o2 = M

o2 : LieAlgebra
i3 : N = lieAlgebra{a1,b1}

o3 = N

o3 : LieAlgebra
i4 : f = mapLie(L,M)

o4 = f

o4 : MapLie
i5 : useLie M

o5 = M

o5 : LieAlgebra
i6 : g = mapLie(M,N,{b,a})

o6 = g

o6 : MapLie
i7 : useLie L

o7 = L

o7 : LieAlgebra
i8 : d = derLie(f,{a a b,b b a,a a b+b b a})

o8 = d

o8 : DerLie
i9 : peekLie d

o9 = a =>  - (a b a)
     b => (b b a)
     c =>  - (a b a) + (b b a)
     maplie => MapLie{a => a        }
                      b => b
                      c => 0
                      sourceLie => M
                      targetLie => L
     sign => 0
     weight => {2, 0}
     sourceLie => M
     targetLie => L
i10 : peekLie(f*g)

o10 = MapLie{a1 => b       }
             b1 => a
             sourceLie => N
             targetLie => L
i11 : h = d*g

o11 = h

o11 : DerLie
i12 : peekLie h

o12 = a1 => (b b a)
      b1 =>  - (a b a)
      maplie => MapLie{a1 => b       }
                       b1 => a
                       sourceLie => N
                       targetLie => L
      sign => 0
      weight => {2, 0}
      sourceLie => N
      targetLie => L