On functional bases of the first-order differential invariants for non-conjugate subgroups of the Poincaré group $P(1,4)$

Abstract

It is established which functional bases of the first-order differential invariants of the splitting and non-splitting subgroups of the Poincaré group $P(1,4)$ are invariant under the subgroups of the extended Galilei group $\widetilde G(1,3) \subset P(1,4)$. The obtained sets of functional bases are classified according to dimensions.