Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit

Abstract

We describe in detail two-parameter nonstandard quantum deformation of D=4 Lorentz algebra $\mathfrak{o}(3,1)$, linked with Jordanian deformation of $\mathfrak{sl}(2;\mathbb{C})$. Using twist quantization technique we obtain the explicit formulae for the deformed coproducts and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with dimensionless deformation parameter. Finally, we interpret $\mathfrak{o}(3,1)$ as the D=3 de-Sitter algebra and calculate the contraction limit $R\to \infty$ ($R$ -- de-Sitter radius) providing explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with masslike deformation parameters), which is the two-parameter light-cone $\kappa$-deformation of the D=3 Poincaré symmetry.

13 pages, no figures

References in corpus (1)

• A Gravity Theory on Noncommutative Spaces

Cited by in corpus (7)

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• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries