Particles of nonzero rest mass and spin algebras

We construct a family of parametrized spin-Z_α algebras from the (canonical) spin-S and (helicity)spin-Z ones in the case of irreducible unitary representations [m, s] of the Poincaré group. The parameter α refers to a rotation angle around the third axis. Equivalences of such constructions are given through a family of unitary transformations containing, for definite values of α, well established and very useful transformations. General formulas referring to the so-called Shirokov-Foldy form of the Poincaré generators and to typical Shirokov's operators are given explicitly.