Two-parameter extensions of the \kappa-Poincar\'{e} quantum deformation

Abstract

We consider the extensions of classical r-matrix for \kappa-deformed Poincar\'{e} algebra which satisfy modified Yang-Baxter equation. Two examples introducing additional deformation parameter (dimensionfull \frac{1}{\widetilde{\kappa}} or dimensionless \xi) are presented. We describe the corresponding quantization (two-parameter \kappa-Poincar\'{e} quantum Hopf algebras) in explicite form as obtained by twisting of standard \kappa-deformed framework. In the second example quantum twist function depends on nonclassical generators, with \kappa-deformed coproduct. Finally we mention also the ``soft'' twists with carrier in fourmomenta sector.