SYM Paclet Symbol

AdjointRepresentationOfAlgebra

AdjointRepresentationOfAlgebra[L]
gives the adjoint representation of the Lie algebra L.

To use AdjointRepresentationOfAlgebra, 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.

suppress printing whether the representation returned is faithfull

AdjointRepresentationOfAlgebra returns a set of matrices that span the adjoint representation of the Lie algebra. A message will be printed inticating wheteher the representation is faithfull. That message can be suppresed with the option Silent.

Let the Lie algebra:

its adjoint representation is given by the span of the matrices:

Let the Lie algebra given by its structure constants:

its adjoint representation is given by the span of the matrices:

Evidently, this Lie algebra is so(3).