D = 4 quantum Poincaré algebras and finite difference time derivatives

The contraction of quantum Lie algebras providing real D = 4 quantum Poincaré algebras are briefly reviewed. The case of κ-deformation of D = 4 Poincaré algebra with flat nonrelativistic sector is described in some detail. The κ-modification of relativistic dynamics consists in introducing in consistent way the finite difference time derivatives. The κ-Lorentz group has a quasigroup structure introduced by Batalin