1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Institute of Physics, Jagiellonian University, Krakow, Poland3 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
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.
Journal of Noncommutative Geometry, 2013, Vol 7, Issue 3, p. 605-645