Pensieve header: Debugging αMap.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\WKO4"];
<< FreeLie.m;
<< AwCalculus.m;
$SeriesShowDegree=4;

Φs[2,1]=Φs[3,1]=Φs[3,2]=0;Φs[3,1,2]=1/24; Φ=DKS[3, Φs];
SeriesSolve[Φ, ((Φ^(σ[3,2,1]))≡-Φ)∧(Φ**(Φ^(σ[1,23,4]))**(Φ^(σ[2,3,4]))≡(Φ^(σ[12,3,4]))**(Φ^(σ[1,2,34])))];
Φ@{6}

αMap[S_List][dks_DKSeries] := Sum[
LieMorphism[
Table[
LW@S[[i]] -> AngleBracket@@Table[
S[[j]]->LS[Switch[j,
i, LW@S[[k]],
k, LW@S[[i]],
 _, 0
]],
 {j, Length[S]}],
{i,k-1}
],
AngleBracket@@S, tb
][(Subscript[dks, S[[k]]])],
{k,2,Length[S]}
]

Ψ=Γ[El[αMap[{1,2,3}][Φ], CWS[0]]]

(Ψ**(Ψ^(σ[1,23,4]))**(Ψ^(σ[2,3,4]))≡(Ψ^(σ[12,3,4]))**(Ψ^(σ[1,2,34])))@{8}

S={1,2,3}; dks=Φ;

k=2

(Subscript[dks, k])

Table[
LW@S[[i]] -> AngleBracket@@Table[
S[[j]]->LS[Switch[j,
i, LW@S[[k]],
k, LW@S[[i]],
 _, 0
]],
 {j, Length[S]}],
{i,k-1}
]

AngleBracket@@Take[S,k]

LieMorphism[
Table[
LW@S[[i]] -> AngleBracket@@Table[S[[j]]->LS[Switch[j, i, LW@S[[k]], k, LW@S[[i]], _, 0]], {j, k}],
{i,k-1}],
AngleBracket@@Take[S,k], tb
]

LieMorphism[
Table[
LW@S[[i]] -> AngleBracket@@Table[S[[j]]->LS[Switch[j, i, LW@S[[k]], k, LW@S[[i]], _, 0]], {j, k}],
{i,k-1}],
AngleBracket@@Take[S,k], tb
][(Subscript[dks, k])]