Differential structure on the $\kappa$-Minkowski spacetime from twist

Abstract

We study four dimensional $\kappa$-Minkowski spacetime constructed by the twist deformation of $U(igl(4,R))$. We demonstrate that the differential structure of such twist-deformed $\kappa$-Minkowski spacetime is closed in four dimensions contrary to the construction of $\kappa$-Poincaré bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.

8pages, no figures, references added,minor corrections

References in corpus (23)

• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Quantum $\kappa$-Poincare in Any Dimensions
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Kappa-Minkowski space-time and the star product realizations
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• Twisted Statistics in kappa-Minkowski Spacetime
• Fock space, quantum fields and kappa-Poincaré symmetries
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• From noncommutative kappa-Minkowski to Minkowski space-time
• Hopf-algebra description of noncommutative-spacetime symmetries
• Generalized Weyl systems and kappa-Minkowski space
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Generalized kappa-deformed spaces, star-products, and their realizations
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• kappa-deformed Spacetime From Twist
• A non-commutative Minkowskian spacetime from a quantum AdS algebra
• Classification of Differential Calculi on U_q(b+), Classical Limits, and Duality
• Differential calculi on quantum Minkowski space
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• $\kappa -$Minkowski spacetime and a uniformly accelerating observer
• Blackbody radiation in κ-Minkowski spacetime
• Density fluctuations in $\kappa$-deformed inflationary universe

Cited by in corpus (25)

• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Kappa-deformed Snyder spacetime
• Rainbow statistics
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• 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
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Quantum statistics and noncommutative black holes
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Differential forms and k-Minkowski spacetime from extended twist
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Dirac Operators on Noncommutative Curved Spacetimes
• Primitively divergent diagrams in $\kappa$-deformed scalar field with quartic self-interaction
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime