Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

Abstract

We construct realizations of the generators of the $\kappa$-Minkowski space and $\kappa$-Poincaré algebra as formal power series in the $h$-adic extension of the Weyl algebra. The Hopf algebra structure of the $\kappa$-Poincaré algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on $\kappa$-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the $\kappa$-Minkowski space.

20 pages. Accepted for publication in International Journal of Modern Physics A

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Cited by in corpus (28)

• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• A twisted look on kappa-Minkowski: U(1) gauge theory
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski
• Nonassociative Snyder phi4 Quantum Field Theory
• Quantum statistics and noncommutative black holes
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• Different realizations of kappa-momentum space and relative-locality effect
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Noncommutative Yang model and its generalizations
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Hermitian realizations of kappa-Minkowski spacetime
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• The Weyl realizations of Lie algebras and left-right duality
• Twist for Snyder space
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• One Parameter Family of Jordanian Twists
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Generalization of Weyl realization to a class of Lie superalgebras
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations
• Realizations of the Extended Snyder Model