Quantum Deformations of Einstein’s Relativistic Symmetries

We shall outline two ways of introducing the modification of Einstein’s relativistic symmetries of special relativity theory the Poincaré symmetries. The most complete way of introducing the modifications is via the noncocommutative Hopfalgebraic structure describing quantum symmetries. Two types of quantum relativistic symmetries are described, one with constant commutator of quantum Minkowski space coordinates (θμν -deformation) and second with Lie-algebraic structure of quantum space-time, introducing so-called κ-deformation. The third fundamental constant of Nature fundamental mass κ or length λ appears naturally in proposed quantum relativistic symmetry scheme. The deformed Minkowski space is described as the representation space (Hopf-module) of deformed Poincaré algebra. Some possible perspectives of quantum-deformed relativistic symmetries will be outlined.