We define a family of star products and involutions associated with -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 -Minkowski space. Furthermore, we give an explicit realization of the action of the -Poincaré algebra as an involutive Hopf algebra on this representation of -Minkowski space and initiate a study of its properties.
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Bergfinnur Durhuus, Andrzej Sitarz, Star product realizations of <var>κ</var>-Minkowski space. J. Noncommut. Geom. 7 (2013), no. 3, pp. 605–645