Generalized Poincaré algebras, Hopf algebras and κ-Minkowski spacetime

We propose a generalized description for the κ-Poincaré-Hopf algebra as a symmetry quantum group of underlying κ-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of κ-Minkowski algebra realization. For the given realization of κ-Minkowski spacetime there is a unique κ-Poincaré-Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with κ-Poincaré algebras which are related to κ-Poincaré-Hopf algebra with undeformed Lorentz algebra. Known bases of κ-Poincaré-Hopf algebra are obtained as special cases. Also deformation of igl(4) Hopf algebra compatible with the κ-Minkowski spacetime is presented. Some physical applications are briefly discussed.