New quantum (anti)de Sitter algebras and discrete symmetries

Abstract

Two new quantum anti-de Sitter so(4,2) and de Sitter so(5,1) algebras are presented. These deformations are called either time-type or space-type according to the dimensional properties of the deformation parameter. Their Hopf structure, universal R matrix and differential-difference realization are obtained in a unified setting by considering a contraction parameter related to the speed of light, which ensures a well defined non-relativistic limit. Such quantum algebras are shown to be symmetry algebras of either time or space discretizations of wave/Laplace equations on uniform lattices. These results lead to a proposal fortime and space discrete Maxwell equations with quantum algebra symmetry.

10 pages, LaTeX

References in corpus (6)

• Deformed Boost Transformations That Saturate at the Planck Scale
• Conformal compactification and cycle-preserving symmetries of spacetimes
• κ-deformations of D=4 Weyl and conformal symmetries
• $\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space
• Planck-scale relativity from quantum $\kappa$-Poincaré algebra
• Kappa - Poincare dispersion relations and the black hole radiation

Cited by in corpus (17)

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• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• A non-commutative Minkowskian spacetime from a quantum AdS algebra
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra
• Contractions, deformations and curvature
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Twisted conformal algebra related to $\kappa$-Minkowski space
• Hamiltonian formalism and spacetime symmetries in generic DSR models
• Twisted Conformal Algebra so(4,2)
• Lifetime of flying particles in canonical Doubly Special Relativity
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré