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

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 superalgebra. 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.

kappa-Minkowski space; Lorenz algebra; realizations; differential algebra; covariance

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