SYM Paclet Symbol

NilpotencyClass

NilpotencyClass[L]
calculates the nilpotency class of the nilpotent Lie algebra L.

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

The Lie algebra L can be given either from its structure constants or from its infinitesimal generator representation.

NilpotencyClass will that the supplied Lie algebra is nillpotent and will return Null otherwise.

Nilpotency class of a nilpotent Lie Algebra L is the smallest number c such that L^c≠0 but L^c+1=0. Where Lⁱ⁺¹=[L, Lⁱ], i>1 and L¹=L.

Let the Lie algbera:

This is indeed a nilpotent algebra:

with nilpotency class: