Construction of θ-Poincaré algebras and their invariants on Mθ

In the present paper we construct deformations of the Poincaré algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate ansatz for the deformed Lorentz generators. They turn out to be equivalent Hopf algebras of quantum universal enveloping algebra type with nontrivial antipodes. In order to present a notion of θ-deformed Minkowski space Mθ, we introduce Casimir operators and a spacetime invariant.