Quantum Lorentz and braided Poincaré groups
نویسنده
چکیده
Quantum Lorentz groups H admitting quantum Minkowski space V are selected. Natural structure of a quantum space G = V × H is introduced, defining a quantum group structure on G only for triangular H (q = 1). We show that it defines a braided quantum group structure on G for |q| = 1.
منابع مشابه
Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group
Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided group versions of the standard quantum groups Uq(g). They have the same FRT generators l± but a matrix braided-coproduct ∆L = L⊗L where L = l+Sl−, and are se...
متن کاملQuantum braided Poincaré group
A new deformation of the of the Poincaré group and of the Minkowski space-time is given. From the mathematical point of view this deformation is rather quantum-braided group. Global and local structure of this quantumbraided Poincaré group is investigated. A kind of “quantum metrics” is introduced in the q-Minkowski space.
متن کاملRepresentations of Lorentz and Poincaré groups
In quantum field theory, we actually consider a subgroup of O(1, 3), the proper orthochronous or restricted Lorentz group SO(1, 3) = {Λ ∈ O(1, 3)| detΛ = 1 and Λ0 ≥ 0}, which excludes parity and time-reversal transformations that are thus considered as separate, discrete operations P and T . A generic element Λ of the Lorentz group is given by exponentiating the generators together with the par...
متن کاملBraided Momentum in the Q-poincare Group
The q-Poincaré group of [1] is shown to have the structure of a semidirect product and coproduct B>⊳ ̃ SOq(1, 3) where B is a braided-quantum group structure on the q-Minkowski space of 4-momentum with braided-coproduct ∆p = p⊗ 1+1⊗p. Here the necessary B is not a usual kind of quantum group, but one with braid statistics. Similar braided-vectors and covectors V (R), V (R) exist for a general R...
متن کاملOn Braided Poisson and Quantum Inhomogeneous Groups
It is well known [1, 2] that the Lorentz part of any quantum (or Poisson) Poincaré group is triangular. This is in fact a general feature, which excludes the standard q-deformation from the context of inhomogeneous quantum groups [3]. In order to make the standard q-deformation compatible with inhomogeneous groups one has to consider some generalization of the notion of quantum (Poisson) group,...
متن کامل