Hello everybody
Maybe someone can help me out here.
I'm trying with Mathematica to compute derivations using structure constants C[i,j][k].
Please How I can write correct and simply this mathematica coding to obtain the same matrices of the derivations of low dimensional associative algebras (See attachment above).
n = 2;
CC = Flatten[Table[c[i, j][k], {i, n}, {j, n}, {k, n}]]
DD = Table[a[i, j], {i, n}, {j, n}]
For[i = 1, i <= n, i++,
For[j = 1, j <= n, j++, For[k = 1, k <= n, k++, c[i, j][k] = 0]]]
c[1, 1][2] = 1;
Der[i_, j_, m_] := \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(k =
1\), \(n\)]\((\(c[i, j]\)[k] a[m, k] - \(c[k, j]\)[m] a[k,
j] - \(c[i, k]\)[m] a[k, j])\)\)
DerSyst =
Union[Flatten[Table[Simplify[Der[i, j, m]], {i, n}, {j, n}, {m, n}]]]
System = {DerSyst}
Sol = Reduce[System == 0, Variables[System]]
Best regards
Bouzid
