I am a Physicist, so probably my question could sound trivial or even stupid to most of you. I apologize in advance. I'm working with a set of quantum-mechanical operators, which realize a 10-dimensional Lie algebra. Starting from the defining commutators between the various operators, is there a way to find a matrix realization of this algebra?

First of all: is there a way to determine the dimension of the square matrices that must be employed?

Can you please suggest me a way, or an "algorithm" to write these 10 matrices?