Differential structure on the $\kappa$-Minkowski spacetime from twist

Abstract

We study four dimensional $\kappa$-Minkowski spacetime constructed by the twist deformation of $U(igl(4,R))$. We demonstrate that the differential structure of such twist-deformed $\kappa$-Minkowski spacetime is closed in four dimensions contrary to the construction of $\kappa$-Poincar\'{e} bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.