SYM Paclet Symbol

CenterofAlgebra

CenterofAlgebra[L]
gives the center of the Lie algebra L.

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

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

CenterofAlgebra returns the span of elements of L that make up the center. Depending on the input, this can be given as a list of infinitesimal generators or by indexing the initial algebra using the symbol X.

The center of a Lie algebra is the set of elements that commute with all the others.

Let the Lie algebra:

The center of this Lie algebra is the empty set:

Let the Lie algebra expressed by its structure constants:

Out[2]=

The center of this Lie algebra is: