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arxiv: 1104.0206 · v1 · pith:Q6H2UBEVnew · submitted 2011-04-01 · 🧮 math-ph · hep-th· math.FA· math.MP· math.QA

Star product realizations of kappa-Minkowski space

classification 🧮 math-ph hep-thmath.FAmath.MPmath.QA
keywords spacealgebrakappastarminkowskiproductsfunctionshopf
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We define a family of star products and involutions associated with $\kappa$-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 $\kappa$-Minkowski space. Furthermore, we give an explicit realization of the action of the $\kappa$-Poincar\'e algebra as an involutive Hopf algebra on this representation of $\kappa$-Minkowski space and initiate a study of its properties.

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