Abstract
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.
| Original language | English |
|---|---|
| Journal | Journal of Noncommutative Geometry |
| Volume | 7 |
| Issue number | 3 |
| Pages (from-to) | 605-645 |
| ISSN | 1661-6952 |
| DOIs | |
| Publication status | Published - 2013 |