Lorentz covariant $\kappa$-Minkowski spacetime

In recent years, different views on the interpretation of Lorentz covariance of noncommuting coordinates have been discussed. By a general procedure, we construct the minimal canonical central covariantization of the $\kappa$-Minkowski spacetime. Here, undeformed Lorentz covariance is implemented by unitary operators, in the presence of two dimensionful parameters. We then show that, though the usual $\kappa$-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a noncovariant restriction of the covariantized model. We conclude with some general comments on the approach of deformed covariance.