Generalized kappa-deformed spaces, star-products, and their realizations

TL;DR

This paper develops a systematic framework for constructing and relating realizations of generalized kappa-deformed noncommutative spaces, including star-products, derivatives, and twist operators, with applications to specific models.

Contribution

It introduces a unified method for realizing noncommutative coordinates and deriving associated algebraic structures, expanding the toolkit for studying deformed spacetime geometries.

Findings

All realizations are connected via similarity transformations.

Explicit forms of star-products and twist operators are derived.

Application to Nappi-Witten type noncommutative space demonstrates the framework's utility.

Abstract

In this work we investigate generalized kappa-deformed spaces. We develop a systematic method for constructing realizations of noncommutative (NC) coordinates as formal power series in the Weyl algebra. All realizations are related by a group of similarity transformations, and to each realization we associate a unique ordering prescription. Generalized derivatives, the Leibniz rule and coproduct, as well as the star-product are found in all realizations. The star-product and Drinfel'd twist operator are given in terms of the coproduct, and the twist operator is derived explicitly in special realizations. The theory is applied to a Nappi-Witten type of NC space.