 Up to formal equivalence, the Moyal Bracket is the "unique one-parameter Lie-algebraic deformation" of the Poisson bracket.Its algebraic isomorphism to the algebra of commutators bypasses the negative result of the Groenewold–van Hove theorem, which precludes such an isomorphism for the Poisson bracket, a question implicitly raised by Dirac in 
his 1926 doctoral thesis