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Would you know an algorithm (or an automatic method) that computes all maximal ideals $J$ of a given Lie algebra?

Or an algorithm that computes all maximal ideals $J$ containing a given minimal ideal $I$?

The input would be the structure constants of the Lie algebra on a given basis (plus a basis of the minimal ideal $I$ in the second case).

Many thanks in advance.

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    $\begingroup$ Have you looked at W.A. de Graaf's book ams.org/mathscinet-getitem?mr=1743970 (or his papers)? $\endgroup$
    – Jim Humphreys
    Commented Jan 19, 2015 at 16:31
  • $\begingroup$ @Jim Thank you for your suggestion. I do not have access to this book, but from the "Contents" and the "Index of Algorithms" at the end, I am not sure that it provides a (straight) answer. I have also read other articles of de Graaf and I did not find anything. $\endgroup$
    – Nina
    Commented Jan 19, 2015 at 16:57
  • $\begingroup$ It might still be helpful to ask him directly by email (I think he is now at the University of Trento in Italy), since he is quite experienced with Lie algebra algorithms. $\endgroup$
    – Jim Humphreys
    Commented Jan 19, 2015 at 18:50
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    $\begingroup$ Yes, he is indeed experienced with it. We discussed an algorithm about finding maximal abelian ideals. I think it can be adapted for the general case. $\endgroup$
    – Dietrich Burde
    Commented Jan 19, 2015 at 21:25
  • $\begingroup$ Many thanks for your advice. I finally found a way to get around this computation for my specific problem. But I will definitely keep the name of de Graaf in mind. $\endgroup$
    – Nina
    Commented Jan 20, 2015 at 16:24

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