Classical basis for kappa-Poincare algebra and doubly special relativity theories

Several issues concerning quantum kappa-Poincare algebra are discussed and reconsidered. We propose two different formulations of kappa-Poincare quantum algebra. Firstly we present complete Hopf algebra formulae of kappa-Poincare in classical Poincare basis. Further by adding one extra generator, modifying the classical structure of Poincare algebra, we eliminate non polynomial functions in the kappa-parameter. Hilbert space representations of such algebras make Doubly Special Relativity (DSR) similar to the Stueckelberg version of relativistic Quantum Mechanics