In this Letter we study an infinite extension of the Galilei symmetry group in any dimension that can be thought of as a nonrelativistic or post-Galilean expansion of the Poincare symmetry. We find an infinite-dimensional vector space on which this generalized Galilei group acts and usual Minkowski space can be modeled by our construction. We also construct particle and string actions that are invariant under these transformations.
J. G. acknowledges the hospitality and support of the Van Swinderen Institute where this work was finished. J. G. also has been supported in part by MINECO FPA2016-76005-C2-1-P and Consolider CPAN, and by the Spanish government (MINECO/FEDER) under Project No. MDM-2014-0369 of ICCUB (Unidad de Excelencia Mara de Maeztu). P. S.-R. acknowledges DI-VRIEA for financial support through Proyecto Postdoctorado 2019 VRIEA-PUCV.