Lie algebra expansions and actions for non-relativistic gravity

This work and LR have been supported in part by the MINECO/FEDER, UE grant FPA2015-66793-P and by the Spanish Research Agency (Agencia Estatal de Investigaci´on) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597. JMI has been supported by the grants MTM2014-57129-C2-1-P from the MINECO (Spain), VA137G18 Spanish Junta de Castilla y Le´on and FEDER BU229P18. TO wishes to thank M.M. Fern´andez for her permanent support. EB wishes to thank the Instituto de F´isica Te´orica UAM/CSIC of Madrid for hospitality.