  Formulating a relativistic equation for particles with arbitrary spin remains
an open challenge in theoretical physics. In this study, the main algebraic
approaches used to generalize the Dirac and Kemmer Duffin equations for
particles of arbitrary spin are investigated. It is proved that an irreducible
relativistic equation formulated using spin matrices satisfying the commutation
relations of the anti-de Sitter group leads to inconsistent results, mainly as
a consequence of violation of unitarity and the appearance of a mass spectrum
that does not reflect the physical reality of elementary particles. However,
the introduction of subsidiary conditions resolves the problem of unitarity and
restores the physical meaning of the mass spectrum. The equations obtained by
these approaches are solved and the physical nature of the solutions is
discussed.
