They are widely used in quantum chromodynamics as an approximate symmetry of the strong interaction between quarks and gluons. The generators of an algebra can be obtained in different ways, but the most commonly used ones in physics are based on a generalization of the Pauli matrices of su(2) and of the Gell-Mann matrices of su (3), which are what we use in this work. This specific way of representing the generators is commonly referred to as the Generalized Gell-Mann matrix (GGM) basis. In the following, we briefly review the general expressions of these GGM generators. The commutation (and anti-commutation) relations among these generators are defined in the su(N ) Lie algebra, whereas the exponential functions of these generators construct the elements of the SU (N ) Lie group via the exponential map. The elements of the GGM basis are denoted as Ŝi with