Hopf-algebra description of noncommutative-spacetime symmetries

Abstract

I give a brief summary of the results reported in hep-th 0306013 in collaboration with G. Amelino-Camelia and F. D'Andrea. I focus on the analysis of the symmetries of $\kappa$-Minkowski noncommutative space-time, described in terms of a Weyl map. The commutative space-time notion of Lie-algebra symmetries must be replaced by the one of Hopf-algebra symmetries. However, in the Hopf algebra sense, it is possible to construct an action in $\kappa$-Minkowski which is invariant under a 10-generators Poincaré-like symmetry algebra.

arXiv comment7 pages, LaTex (To appear in the proceedings of 12-th International Colloquium "Quantum Groups and Integrable Systems", Prague, 12-14 June 2003.)

References in corpus (8)

• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Non-commutative space-time of Doubly Special Relativity theories
• Generalized Weyl systems and kappa-Minkowski space
• Classification of Differential Calculi on U_q(b+), Classical Limits, and Duality

Cited by in corpus (7)

• The Search for Quantum Gravity Signals
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• The UV/IR Interplay in Theories with Space-time Varying Non-commutativity
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• An Introduction to Noncommutative Physics
• Non-linear quantum mechanics and high energy cosmic rays
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects