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GradedLieAlgebras :: DerLie

DerLie -- a Type for derivations in Lie algebras

Description

This Type represents derivations d from M to L, where M and L are Lie algebras. There is also a homomorphism f from M to L defining L as an M-module (f is the identity for the case of ordinary derivations from L to L). The derivation law reads
d[x,y]=[dx,fy]+/- [fx,dy]
where the sign is determined by the sign of interchanging d and x.

i1 : L = lieAlgebra{a,b}

o1 = L

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

o2 = M

o2 : LieAlgebra
i3 : f = mapLie(L,M)

o3 = f

o3 : MapLie
i4 : useLie L

o4 = L

o4 : LieAlgebra
i5 : der = derLie(f,{a a b,b b a,a a b+b b a})

o5 = der

o5 : DerLie
i6 : peekLie der

o6 = 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
i7 : useLie M

o7 = M

o7 : LieAlgebra
i8 : der a c

o8 =  - (a a b a) + (b a b a)

o8 : L

See also

Functions and methods returning an object of class DerLie :

Methods that use an object of class DerLie :

For the programmer

The object DerLie is a type, with ancestor classes MutableHashTable < HashTable < Thing.