Dual $\kappa$-Minkowski spaces and $\kappa$-Poincar\'{e} algebras from Yang model and their Weyl realizations

Abstract

We consider the Yang algebras isomorphic to $o(1,5), o(2,4), o(3,3)$ and derive dual $\kappa$-Minkowski and $\kappa$-Poincar\'{e} algebras in terms of a metric $g$. The corresponding Weyl realization is presented and coproduct, star product and twist are computed in terms of the metric $g$. Finally, we construct reduced $\kappa$-Minkowski and $\kappa$-Poincar\'{e} algebras as special cases.