  The spin of particles on a non-commutative geometry is investigated within
the framework of the representation theory of the q-deformed Poincare algebra.
An overview of the q-Lorentz algebra is given, including its representation
theory with explicit formulas for the q-Clebsch-Gordan coefficients. The
vectorial form of the q-Lorentz algebra (Wess), the quantum double form
(Woronowicz), and the dual of the q-Lorentz group (Majid) are shown to be
essentially isomorphic. The construction of q-Minkowski space and the
q-Poincare algebra is reviewed. The q-Euclidean sub-algebra, generated by
rotations and translations, is studied in detail. The results allow for the
construction of the q-Pauli-Lubanski vector, which, in turn, is used to
determine the q-spin Casimir and the q-little algebras for both the massive and
the massless case. Irreducible spin representations of the q-Poincare algebra
are constructed in an angular momentum basis, accessible to physical
interpretation. It is shown how representations can be constructed,
alternatively, by the method of induction. Reducible representations by
q-Lorentz spinor wave functions are considered. Wave equations on these spaces
are found, demanding that the spaces of solutions reproduce the irreducible
representations. As generic examples the q-Dirac equation and the q-Maxwell
equations are computed explicitly and their uniqueness is shown.
