Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation

Abstract

This paper together with the previous one (arXiv:hep-th/0604146) presents the detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf algebra in terms of complex and real generators. We describe here in detail two quantum deformations of the D=4 Lorentz algebra o(3,1) obtained by twisting of the standard q-deformation U_{q}(o(3,1)). For the first twisted q-deformation an Abelian twist depending on Cartan generators of o(3,1) is used. The second example of twisting provides a quantum deformation of Cremmer-Gervais type for the Lorentz algebra. For completeness we describe also twisting of the Lorentz algebra by standard Jordanian twist. By twist quantization techniques we obtain for these deformations new explicit formulae for the deformed coproducts and antipodes of the o(3,1)-generators.

17 pages

References in corpus (5)

• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Special Reduced Multiplets and Minimal Representations for SO(p,q)
• Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
• On Twist Quantizations of D=4 Lorentz and Poincare Algebras

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• Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Quantum deformations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries in unified $\mathfrak{o}(4;\mathbb{C})$ setting -- Addendum
• Quantizations of D=3 Lorentz symmetry
• Two-particle system in noncommutative space with preserved rotational symmetry
• Time correlation functions and Fisher zeros for q-deformed Bose gas
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries