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.
Categories: hep-th