On the classification of quantum Poincaré groups

Abstract

Using the general theory of [10] ( hep-th 9412058 ), quantum Poincaré groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most cases we solve them and give the classification of quantum Poincaré groups. Each of them corresponds to exactly one quantum Minkowski space. The Poincaré series of these objects are the same as in the classical case. We also classify possible $R$-matrices for the fundamental representation of the group.

31 pages, LaTeX file, minor changes in Remarks 1.7-8

References in corpus (1)

• Braided Momentum Structure of the q-Poincare Group

Cited by in corpus (51)

• Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• Diffeomorphisms in group field theories
• Doubly Special Relativity versus $\kappa$-deformation of relativistic kinematics
• Poisson structures on the Poincare group
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• Scalar field theory in Snyder space-time: alternatives
• Space-time symmetry of noncommutative field theory
• κ-deformations of D=4 Weyl and conformal symmetries
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Distance Measurement and $\kappa$-Deformed Propagation of Light and Heavy Probes
• Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces
• Quantum (1+1) extended Galilei algebras: from Lie bialgebras to quantum R-matrices and integrable systems
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Relativistic and Newtonian kappa spacetimes
• Introduction to quantum groups
• On the structure of inhomogeneous quantum groups
• Noncommutative Geometry for Pedestrians
• On crossed product of algebras
• Classification of Low Dimensional Lie Super-Bialgebras
• Algebraic approach to quantum gravity II: noncommutative spacetime
• On the physical contents of q-deformed Minkowski spaces
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Quantum groups and deformed special relativity
• Deformed Minkowski spaces: clasification and properties
• Global Symmetries of Noncommutative Space-time
• Poisson Poincare groups
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• k-deformed Poincare algebras and quantum Clifford-Hopf algebras
• All noncommutative spaces of $\kappa$-Poincaré geodesics
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• Deformations of Euclidean Supersymmetries
• Central tetrads and quantum spacetimes
• Quantum groups with projection and extensions of locally compact quantum groups
• Noncommutative Parameters of Quantum Symmetries and Star Products
• Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincare / super-Euclidean r-matrices
• Deformed Galilei symmetry
• The Dirac operator and gamma matrices for quantum Minkowski spaces
• Classification of real three-dimensional Poisson-Lie groups
• The noncommutative space of light-like worldlines
• Extensions of Peripheric Extended Twists and Inhomogeneous Lie Algebras
• Quantum Lorentz and braided Poincare groups
• Quasitriangularity and enveloping algebras for inhomogeneous quantum groups
• A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• On the Quantum Lorentz Group
• On braided Poisson and quantum inhomogeneous groups