Dynamical symmetries in noncommutative theories

In the present work we study dynamical space-time symmetries in noncommutative relativistic theories by using the minimal canonical extension of the Doplicher, Fredenhagen and Roberts algebra. Our formalism is constructed in an extended space-time with independent degrees of freedom associated with the object of noncommutativity ${\theta }^{\mu \nu }$. In this framework we consider theories that are invariant under the Poincar'{e} group $\mathcal{P}$ or under its extension ${\mathcal{P}}^{\mathrm{\prime }}$, when translations in the extra dimensions are permitted. The Noether’s formalism adapted to such extended $x+\theta$ space-time is employed.