  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.
