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.

arXiv comment13 pages, no figures

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Cited by in corpus (14)

• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• On second quantization on noncommutative spaces with twisted symmetries
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• On Light-like Deformations of the Poincaré Algebra