  Superconducting quantum symmetries in extended single-band 1-dimensional
Hubbard models are shown to originate from the classical (pseudo-)spin SO(4)
symmetry of a class of models of which the standard Hubbard model is a special
case. Extending the notion of symmetry to include quantum groups allows us to
introduce extra parameters but the corresponding quantum symmetric models are
restricted to one dimension. All models discussed are related by generalized
Lang-Firsov transformations, some have symmetries away from half filling. The
most general model with symmetric next-neighbour interaction terms and
classical SO(4) symmetry is given explicitly.
