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

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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 Poincar\{e} 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 Poincar\{e} algebra with masslike deformation parameters, which is the two-parameter light-cone $\kappa$-deformation of the D=3 Poincar\{e} symmetry.

Autor: A. Borowiec; J. Lukierski; V. N. Tolstoy

Fuente: https://archive.org/