Star product realizations of kappa-Minkowski space
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Star product realizations of kappa-Minkowski space. / Durhuus, Bergfinnur; Sitarz, Andrzej .
I: Journal of Noncommutative Geometry, Bind 7, Nr. 3, 2013, s. 605-645.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Star product realizations of kappa-Minkowski space
AU - Durhuus, Bergfinnur
AU - Sitarz, Andrzej
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
U2 - 10.4171/JNCG/129
DO - 10.4171/JNCG/129
M3 - Journal article
VL - 7
SP - 605
EP - 645
JO - Journal of Noncommutative Geometry
JF - Journal of Noncommutative Geometry
SN - 1661-6952
IS - 3
ER -
ID: 103901755