The generators of M=f.sourceLie are mapped to the elements in the last argument defs and they should be given as generalExpressionLie in L=f.targetLie. 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). The set of elements of class DerLie is a Lie algebra with Lie multiplication multDerLie, however it does not belong to LieAlgebra if we do not have a finite presentation. It is checked by the program that d maps the relations in d.sourceLie to zero.
i1 : L=lieAlgebra({x,y},{},genSigns=>1)
o1 = L
o1 : LieAlgebra
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i2 : M=lieAlgebra({a,b},{[b,a,b]},genSigns=>0,genWeights=>{2,2})
o2 = M
o2 : LieAlgebra
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i3 : f = mapLie(L,M,{[x,x],[]})
o3 = f
o3 : MapLie
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i4 : d1 = derLie(f,{[x,x],[x,y]})
o4 = d1
o4 : DerLie
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i5 : peek d1
o5 = DerLie{[b, a, b] => [] }
a => [x, x]
b => [x, y]
maplie => f
signDer => 0
sourceLie => M
targetLie => L
weightDer => {0, 0}
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i6 : evalDerLie(d1,[a,a,b])
o6 = {{-2}, {[x, x, x, y, x, x]}}
o6 : List
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i7 : useLie L o7 = L o7 : LieAlgebra |
i8 : d2 = derLie({[x,x,y],[x,x,y]})
o8 = d2
o8 : DerLie
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i9 : peek d2
o9 = DerLie{maplie => MapLie{...4...}}
signDer => 0
sourceLie => L
targetLie => L
weightDer => {2, 0}
x => [x, x, y]
y => [x, x, y]
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i10 : peek d2.maplie
o10 = MapLie{sourceLie => L}
targetLie => L
x => [x]
y => [y]
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i11 : evalDerLie(d2,[x,x,y])
1 1
o11 = {{- -, -}, {[x, x, y, x, x], [y, x, y, x, x]}}
2 2
o11 : List
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