The Null Decomposition of Conformal Algebras
  We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its Poincare subalgebra together with a vector operator. The special cases of the conformal algebras of two and three dimensions are described in detail, including the construction of their Casimir operators. 
Dana Mihai, George A.J. Sparling