Star product realizations of kappa-Minkowski space

We define a family of star products and involutions associated with $κ$-Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is demonstrated that they can be extended to a class of polynomially bounded smooth functions allowing a realization of the full Hopf algebra structure on $κ$-Minkowski space. Furthermore, we give an explicit realization of the action of the $κ$-Poincaré algebra as an involutive Hopf algebra on this representation of $κ$-Minkowski space and initiate a study of its properties.

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