SYM Paclet Symbol

UpperCentralSeries

UpperCentralSeries[L]
gives the upper central series for the Lie algebra L.

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

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

To use UpperCentralSeries, 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.

UpperCentralSeries returns the sequence of ideals C₁(L)C₂(L) C_i(L) where, C_i+1(L)/C_i(L)=C(L/C_i(L)), i≥1 and C₁(L)=C(L) the center of 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:

To get the chain up to the second member:

To get only the third member of the chain: