Editing Lie algebra (section)

===Representation theory in physics===
The representation theory of Lie algebras plays an important role in various parts of theoretical physics. There, one considers operators on the space of states that satisfy certain natural commutation relations. These commutation relations typically come from a symmetry of the problem—specifically, they are the relations of the Lie algebra of the relevant symmetry group. An example is the [[angular momentum operator]]s, whose commutation relations are those of the Lie algebra <math>\mathfrak{so}(3)</math> of the rotation group <math>\mathrm{SO}(3)</math>. Typically, the space of states is far from being irreducible under the pertinent operators, but
one can attempt to decompose it into irreducible pieces. In doing so, one needs to know the irreducible representations of the given Lie algebra. In the study of the [[Hydrogen-like atom|hydrogen atom]], for example, quantum mechanics textbooks classify (more or less explicitly) the finite-dimensional irreducible representations of the Lie algebra <math>\mathfrak{so}(3)</math>.<ref name="quantum" />