SYM Paclet Symbol

ChangeBaseOfAlgebra

ChangeBaseOfAlgebra[algebra, newBase]
gives the structure constants for the Lie algebra algebra for a different choice for base.

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

algebra is given by its structure constants. As for the new base, it is defined by using linear combinations of the index symbol X.

Let the Lie algbera:

with structure constants:

Out[3]=

The structure constants of this Lie algebra after interchanging the second and fifth element is:

this can be easily seen by looking between the commutator tables for the two sets of structure constants.

Let the Lie algbera:

with structure constants:

Out[3]=

the structure constants of the algebra spanned by a different base is: