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Generalized kappa-deformed spaces, star products and their realizations. (English) Zbl 1140.81419

Summary: 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 operators 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.

MSC:

81R60 Noncommutative geometry in quantum theory
81S10 Geometry and quantization, symplectic methods
53D55 Deformation quantization, star products
81R25 Spinor and twistor methods applied to problems in quantum theory