Jordanian twist quantization of D=4 Lorentz and Poincaré algebras and D=3 contraction limit
Institute for Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50–205, Wrocław, Poland
2 Institute of Nuclear Physics, Moscow State University, 119992, Moscow, Russia
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Published online: 24 October 2006
We describe in detail the two-parameter nonstandard quantum deformation of the D=4 Lorentz algebra , linked with a Jordanian deformation of . 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 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with a dimensionless deformation parameter. Finally, we interpret as the D=3 de Sitter algebra and calculate the contraction limit (R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with mass-like deformation parameters), which is the two-parameter light-cone κ-deformation of the D=3 Poincaré symmetry.
© Springer-Verlag Berlin Heidelberg, 2006