Canonical and Lie-algebraic twist deformations of $\kappa$-Poincare and contractions to $\kappa$-Galilei algebras

Abstract

We propose canonical and Lie-algebraic twist deformations of $\kappa$-deformed Poincare Hopf algebra which leads to the generalized $\kappa$-Minkowski space-time relations. The corresponding deformed $\kappa$-Poincare quantum groups are also calculated. Finally, we perform the nonrelativistic contraction limit to the corresponding twisted Galilean algebras and dual Galilean quantum groups.

arXiv comment16 pages, no figures, v3: few changes provided - version for journal, v2: submitted incidentally, v4: the page numbers for all references in preprint version are provided

References in corpus (21)

• The quantum structure of spacetime at the Planck scale and quantum fields
• High-Energy Tests of Lorentz Invariance
• Testable scenario for Relativity with minimum-length
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Non-commutative superspace from string theory
• Deformed Boost Transformations That Saturate at the Planck Scale
• New Tests of Lorentz Invariance Following from Observations of the Highest Energy Cosmic Gamma Rays
• An infrared background--TeV gamma-ray crisis?
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Quantum-Gravity Phenomenology: Status and Prospects
• Fock space, quantum fields and kappa-Poincaré symmetries
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Cosmic rays and TeV photons as probes of quantum properties of space-time
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• Twisted Classical Poincaré Algebras
• Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists
• Relativistic and Newtonian kappa spacetimes
• Deformed and extended Galilei group Hopf algebras

Cited by in corpus (13)

• The kappa-(A)dS quantum algebra in (3+1) dimensions
• The $\kappa$-(A)dS noncommutative spacetime
• Drinfel'd doubles for (2+1)-gravity
• On quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Quantum algebras as quantizations of dual Poisson-Lie groups
• Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei
• The noncommutative space of light-like worldlines
• 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