Relativistic and Newtonian kappa spacetimes

Abstract

The deformations of the Galilei algebra and their associated noncommutative Newtonian spacetimes are investigated. This is done by analyzing the possible nonrelativistic limits of an eleven generator (pseudo)extended \kap-Poincar\'e algebra $\tilde{\cal P}_\kappa$ and their implications for the existence of a first order differential calculus. The additional one-form needed to achieve a consistent calculus on \kap-Minkowski space is shown to be related to the additional central generator entering in the $\tilde{\cal P}_\kappa$ Hopf algebra. In the process, deformations of the extended Galilei and Galilei algebras are introduced which have, respectively, a cocycle and a bicrossproduct structure.