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GradedLieAlgebras :: MapLie * DerLie

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

Synopsis

Description

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

i1 : L = lieAlgebra{a,b}

o1 = L

o1 : LieAlgebra
i2 : M = L

o2 = L

o2 : LieAlgebra
i3 : d = derLie{a a b,b b a}

o3 = d

o3 : DerLie
i4 : peekLie d

o4 = a =>  - (a b a)
     b => (b b a)
     maplie => id
     sign => 0
     weight => {2, 0}
     sourceLie => L
     targetLie => L
i5 : N = lieAlgebra{a1,b1}

o5 = N

o5 : LieAlgebra
i6 : g = mapLie(N,L,{b1,a1})

o6 = g

o6 : MapLie
i7 : h = g*d

o7 = h

o7 : DerLie
i8 : peekLie h

o8 = a => (b1 b1 a1)
     b =>  - (a1 b1 a1)
     maplie => MapLie{a => b1       }
                      b => a1
                      sourceLie => L
                      targetLie => N
     sign => 0
     weight => {2, 0}
     sourceLie => L
     targetLie => N