Star product realizations of kappa-Minkowski space

Understand

We define a family of star products and involutions associated with $\kappa$-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 $\kappa$-Minkowski space.
• Furthermore, we give an explicit realization of the action of the $\kappa$-Poincar\'e algebra as an involutive Hopf algebra on this representation of $\kappa$-Minkowski space and initiate a study of its properties.