Suppose we have a Lie algebra with structure constants


$$\mathrm{d}e^i=\sum\_{j<k}a\_{ijk}e^j\wedge e^k$$


for some coefficients $a\_{ijk}$.


In this setting, **how may be checked (perhaps computationally?) that our algebra is nilpotent?** I wonder whether there is a somewhat nice algorithm involving the coefficients.


Thank you for your attention and answers.



Nilpotency of Lie Algebra from Structure Constants
By Engel's theorem, the Lie algebra is nilpotent just when, for any fixed $k$, the matrix $A\_k=(a\_{ijk})$ is nilpotent.


Edit: By Engel's theorem, the Lie algebra is nilpotent just when every linear combination of the matrices $A\_k=(a\_{ijk})$ is nilpotent.


