Differential algebras on kappa-Minkowski space and action of the Lorentz algebra

Abstract

We propose two families of differential algebras of classical dimension on kappa-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl super-algebra. We also propose a novel realization of the Lorentz algebra so(1,n-1) in terms of Grassmann-type variables. Using this realization we construct an action of so(1,n-1) on the two families of algebras. Restriction of the action to kappa-Minkowski space is covariant. In contrast to the standard approach the action is not Lorentz covariant except on constant one-forms, but it does not require an extra cotangent direction.

16 pages

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Cited by in corpus (14)

• 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
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Entanglement dynamics in $\kappa$-deformed spacetime
• Noncommutative Differentials on Poisson-Lie groups and pre-Lie algebras
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• The Weyl realizations of Lie algebras and left-right duality
• Central tetrads and quantum spacetimes
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Generalization of Weyl realization to a class of Lie superalgebras