THE CLASSICAL BASIS FOR κ-DEFORMED POINCARÉ ALGEBRA AND SUPERALGEBRA

Abstract

We describe here the general solution describing generators of κ-deformed Poincaré algebra as the functions of classical Poincaré algebra generators as well as the inverse formulas. Further we present analogous relations for the generators of N=1, D=4 κ-deformed Poincaré superalgebra expressed by the classical Poincaré superalgebra generators. In such a way we obtain the κ-deformed Poincaré (super)algebras with all the quantum deformation present only in the co-algebra sector. As an application we use the classical basis of κ-deformed Poincaré superalgebra for obtaining a new result: the κ-deformation of supersymmetric spin (Pauli-Lubanski) Casimir.