SYM Paclet Symbol

LowerCentralSeries

LowerCentralSeries[L]
gives the lower central series for the Lie algebra L.

LowerCentralSeries[L, n]
gives the lowered central series for the Lie algebra L up to order n.

LowerCentralSeries[L, {n}]
gives the n^th member of the lowered central series for the Lie algebra L.

To use LowerCentralSeries, 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.

LowerCentralSeries returns the sequence of ideals L² Lⁱ where, Lⁱ⁺¹=[L, Lⁱ], i≥1 and L¹=L. The second argument specifies whether a portion or a specific member of the chain will be returned.

Let the Lie algebra defined by the structure constants:

The lower central series is:

It is evident that the Lie algebra is not nilpotent. To get the chain up to the first member other than the Lie algebra:

To get only the second member of the chain: