The classical basis for $\kappa$-deformed Poincar\'e (super)algebra and the second $\kappa$-deformed supersymmetric Casimir

Abstract

We present here the general solution describing generators of \kdef \poin algebra as the functions of classical \poin algebra generators as well as the inverse formulae. Further we present analogous relations for the generators of N=1 D=4 \kdef \poin superalgebra expressed by the classical \poin superalgebra generators. In such a way we obtain the \kdef \poin (super)algebras with all the quantum deformation present only in the coalgebra sector. Using the classical basis of \kdef \poin superalgebra we obtain as a new result the $\k$-deformation of supersymmetric covariant spin square Casimir.