Star product realizations of kappa-Minkowski space
Bergfinnur Durhuus, Andrzej Sitarz

TL;DR
This paper introduces new star products for $$-Minkowski space, demonstrating their algebraic properties, extensions to smooth functions, and explicit realization of the $$-Poincare9 algebra acting on this space.
Contribution
It defines a family of star products and involutions for $$-Minkowski space, showing their algebraic structures and explicit realizations of the $$-Poincare9 algebra.
Findings
Star products have isomorphic Banach algebra completions.
Certain star products extend to polynomially bounded smooth functions.
Explicit realization of $$-Poincare9 algebra action on the space.
Abstract
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 -Poincar\'e algebra as an involutive Hopf algebra on this representation of -Minkowski space and initiate a study of its properties.
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