SYM Paclet Symbol

NilpotentAlgebraQ

NilpotentAlgebraQ[L]
gives True if the Lie algebra L is nilpotent and False otherwise.

To use NilpotentAlgebraQ, you first need to load the SYM Package using Needs["SYM`"].

The Lie algebra L can be provided either from their structure constants or their infinitesimal generator representation.

A Lie algebra L is nilpotent when the chain of ideals L[L, L][L, [L, L]]... terminates to the null set.

Let the Lie algebra:

This is not a nilpotent algebra

Let the Lie algebra:

it is evident from its commutator table that it is solvable

Indeed,