Star product realizations of kappa-Minkowski space

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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 languageEnglish
JournalJournal of Noncommutative Geometry
Issue number3
Pages (from-to)605-645
Publication statusPublished - 2013

ID: 103901755