QUANTUM GROUPS AND DEFORMED SPECIAL RELATIVITY

The structure and properties of possible q-Minkowski spaces are review ed and the corresponding non-commutative differential calculi are deve loped in detail and compared with already existing proposals. This is done by stressing the covariance properties of these algebras with res pect to the corresponding q-deformed Lorentz groups as described by ap propriate reflection equations. This allow us to give an unified treat ment for different q-Minkowski algebras. Some isomorphisms among the s pace-time and derivative algebras are demonstrated, and their represen tations are described briefly. Finally, some. physical consequences an d open problems are discussed.