  In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2)
symmetries of the Dirac equation with scalar and vector potentials. These
symmetries, known as pseudospin and spin symmetries, have been extensively
researched and applied to several physical systems. Twenty years after, in
1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic
symmetry of the atomic nuclei when it is described by relativistic mean field
hadronic models. The main feature of these symmetries is the suppression of the
spin-orbit coupling either in the upper or lower components of the Dirac
spinor, thereby turning the respective second-order equations into
Schr\"odinger-like equations, i.e, without a matrix structure. In this paper we
propose a generalization of these SU(2) symmetries for potentials in the Dirac
equation with several Lorentz structures, which also allow for the suppression
of the matrix structure of second-order equation equation of either the upper
or lower components of the Dirac spinor. We derive the general properties of
those potentials and list some possible candidates, which include the usual
spin-pseudospin potentials, and also 2- and 1-dimensional potentials. An
application for a particular physical system in two dimensions, electrons in
graphene, is suggested.
