The generators of M=f.sourceLie are mapped to the elements in L=f.targetLie given in the last argument defs. It is checked by the program that d maps the relations in d.sourceLie to zero. If no f of class MapLie is given, then the current Lie algebra L is used and the derivation d maps L to L (and f is the identity map). In this latter case, the set of elements of class DerLie is a Lie algebra with Lie multiplication DerLie DerLie. If L has a differential δ, then DerLie is a differential Lie algebra with differential d->[δ,d]. However DerLie does not belong to LieAlgebra unless a positively graded finite presentation can be given.
i1 : L=lieAlgebra({x,y},genSigns=>1) o1 = L o1 : LieAlgebra |
i2 : M=lieAlgebra({a,b},genSigns=>0,genWeights=>{2,2})/{b a b} o2 = M o2 : LieAlgebra |
i3 : f = mapLie(L,M,{x x,L.zz}) o3 = f o3 : MapLie |
i4 : d1 = derLie(f,{x,y}) o4 = d1 o4 : DerLie |
i5 : peekLie d1 o5 = a => x b => y maplie => MapLie{a => (x x) } b => 0 sourceLie => M targetLie => L sign => 1 weight => {-1, 0} sourceLie => M targetLie => L |
i6 : d1 a b o6 = - (y x x) o6 : L |
i7 : useLie L o7 = L o7 : LieAlgebra |
i8 : d2 = derLie({x,y}) o8 = d2 o8 : DerLie |
i9 : peekLie d2 o9 = x => x y => y maplie => id sign => 0 weight => {0, 0} sourceLie => L targetLie => L |
i10 : d2 y y x o10 = 3 (y y x) o10 : L |