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