Star product realizations of kappa-Minkowski space

Bergfinnur Durhuus; Andrzej  Sitarz

doi:10.4171/JNCG/129

Star product realizations of kappa-Minkowski space

Bergfinnur Durhuus, Andrzej Sitarz

Institut for Matematiske Fag

17 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Journal of Noncommutative Geometry
Vol/bind	7
Udgave nummer	3
Sider (fra-til)	605-645
ISSN	1661-6952
DOI	https://doi.org/10.4171/JNCG/129
Status	Udgivet - 2013

Adgang til dokumentet

10.4171/JNCG/129

Citationsformater

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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.

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