On kappa-deformation and triangular quasibialgebra structure

Abstract

We show that, up to terms of order 1/kappa^5, the kappa-deformed Poincare algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders. In the context of kappa-deformed quantum field theory, we argue that this structure, assuming it exists to all orders, ensures that states of any number of identical particles, in any representation, can be defined in a kappa-covariant fashion.

17 pages, Latex, typos corrected, references added, misleading comments on twisting removed

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• Anatomy of a deformed symmetry: field quantization on curved momentum space
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• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Newton's Equation on the kappa space-time and the Kepler problem
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Rainbow statistics
• $\kappa$-deformed Dirac Equation
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Different realizations of kappa-momentum space and relative-locality effect
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• Beyond Fock space in three dimensional semiclassical gravity
• Hermitian realizations of kappa-Minkowski spacetime
• Quantum particles in non-commutative space-time: an identity crisis
• Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
• Integrable Hopf twists, marginal deformations and generalised geometry
• kappa-Deformed Oscillators: Deformed Multiplication Versus Deformed Flip Operator and Multiparticle Clusters
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Braided algebras and the kappa-deformed oscillators
• Three-dimensional gravity and deformations of relativistic symmetries
• The covariant and on-shell statistics in kappa-deformed spacetime
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime