Differential forms and k-Minkowski spacetime from extended twist

Abstract

We analyze bicovariant differential calculus on $\kappa$-Minkowski spacetime. It is shown that corresponding Lorentz generators and noncommutative coordinates compatible with bicovariant calculus cannot be realized in terms of commutative coordinates and momenta. Furthermore, $\kappa$-Minkowski space and NC forms are constructed by twist related to a bicrossproduct basis. It is pointed out that the consistency condition is not satisfied. We present the construction of $\kappa$-deformed coordinates and forms (super-Heisenberg algebra) using extended twist. It is compatible with bicovariant differential calculus with $\kappa$-deformed $\mathfrak{igl}(4)$-Hopf algebra. The extended twist leading to $\kappa$-Poincaré-Hopf algebra is also discussed.

15 pages, minor typos corrected to match the published version

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Cited by in corpus (14)

• On the $\kappa$-Dirac Oscillator revisited
• 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
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• The 2D $\kappa$-Dirac oscillator
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Effects of quantum deformation on the integer quantum Hall effect
• Accelerated horizons and Planck-scale kinematics
• Central tetrads and quantum spacetimes
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Dirac Operators on Noncommutative Curved Spacetimes