Fermions and noncommutative theories

By using a framework where the object of noncommutativity θμν represents independent degrees of freedom, we study the symmetry properties of an extended x+θ space-time, given by the group P', which has the Poincare group P as a subgroup. In this process we use the minimal canonical extension of the Doplicher-Fredenhagen-Roberts algebra. It is also proposed a generalized Dirac equation, where the fermionic field depends not only on the ordinary coordinates but on θμν as well. The dynamical symmetry content of such fermionic theory is discussed, and we show that its action is invariant under P'