We study a Lie algebra type κ-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. PACS number(s):

In this work we investigate generalized kappa-deformed spaces. We develop a systematic method for constructing realizations of noncommutative (NC) coordinates as formal power series in the Weyl algebra. All realizations are related by a group of similarity transformations, and to each realization we associate a unique ordering prescription. Generalized derivatives, the Leibniz rule and coproduct, as well as the star-product are found in all realizations. The starproduct and Drinfel'd twist operator are given in terms of the coproduct, and the twist operator is derived explicitly in special realizations. The theory is applied to a Nappi-Witten type of NC space.

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher-order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded-commutative, but they satisfy the graded Jacobi identity.We also consider the star-product of classical differential forms. The starproduct is well-defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.

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

We propose two families of differential algebras of classical dimension on κ-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 κ-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.