Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime

Abstract

We propose a generalized description for the kappa-Poincare-Hopf algebra as a symmetry quantum group of underlying kappa-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of kappa-Minkowski algebra realization. For the given realization of kappa-Minkowski spacetime there is a unique kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with kappa-Poincare algebras which are related to kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. Known bases of kappa-Poincare-Hopf algebra are obtained as special cases. Also deformation of igl(4) Hopf algebra compatible with the kappa-Minkowski spacetime is presented. Some physical applications are briefly discussed.

15 pages; journal version; Physics Letters B (2012)

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• On the $\kappa$-Dirac Oscillator revisited
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• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Unified description for kappa-deformations of orthogonal groups
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
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• The 2D $\kappa$-Dirac oscillator
• Remarks on simple interpolation between Jordanian twists
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Entanglement dynamics in $\kappa$-deformed spacetime
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• Deformed symmetries in noncommutative and multifractional spacetimes
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• Vector-like deformations of relativistic quantum phase-space and relativistic kinematics
• Differential forms and k-Minkowski spacetime from extended twist
• Spectral dimension with deformed spacetime signature
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Effects of quantum deformation on the integer quantum Hall effect
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Hermitian realizations of kappa-Minkowski spacetime
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Photonic realization of the kappa-deformed Dirac equation
• Twist for Snyder space
• Maximal acceleration in non-commutative space-time and its implications
• Emergence of maximal acceleration from non-commutativity of space-time
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• One Parameter Family of Jordanian Twists
• Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence
• Quantisation of $\kappa$-deformed Dirac equation
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations
• Semiclassical Length Measure from a Quantum-Gravity Wave Function