next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: DerLie

DerLie -- a Type for Lie algebra derivations

Description

This Type represents graded derivations d:M->L where M,L are graded (differential) Lie algebras and L is an M-module via f:M->L. If M=L and f is the identity, the set of elements of class DerLie is a Lie algebra with Lie multiplication multDerLie. However it is not of class LieAlgebra, if we do not have a finite presentation.

i1 : L=lieAlgebra({x,y},{},genSigns=>1)

o1 = L

o1 : LieAlgebra
i2 : M=lieAlgebra({a,b},{},genSigns=>0,genWeights=>{2,2})

o2 = M

o2 : LieAlgebra
i3 : f = mapLie(L,M,{[x,x],[]})

o3 = f

o3 : MapLie
i4 : d = derLie(f,{[x,x],[x,y]})

o4 = d

o4 : DerLie
i5 : peek f

o5 = MapLie{a => [x, x]   }
            b => []
            sourceLie => M
            targetLie => L
i6 : peek d

o6 = DerLie{a => [x, x]        }
            b => [x, y]
            maplie => f
            signDer => 0
            sourceLie => M
            targetLie => L
            weightDer => {0, 0}
i7 : evalDerLie(d,[a,b])

o7 = {{-1}, {[x, y, x, x]}}

o7 : List

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.