Jordanian twist quantization of D=4 Lorentz and Poincare algebras and D=3 contraction limit

We describe in detail the two-parameter nonstandard quantum deformation of the D = 4 Lorentz algebra o( 3, 1), linked with a Jordanian deformation of sl( 2; C). Using the twist quantization technique we obtain the explicit formulae for the deformed co-products and antipodes. Further extending the considered deformation to the D = 4 Poincare algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with a dimensionless deformation parameter. Finally, we interpret o( 3, 1) as the D = 3 de Sitter algebra and calculate the contraction limit R ->infinity ( R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D = 3 Poincare algebra ( with mass-like deformation parameters), which is the two-parameter light-cone deformation of the D = 3 Poincare symmetry.