Galilean W3 algebra

Galilean W-3 vertex operator algebra (VOA) GW(3)(c(L),c(M)) is constructed as a universal enveloping vertex algebra of certain non-linear Lie conformal algebra. It is proved that this algebra is simple by using the determinant formula of the vacuum module. The reducibility criterion for Verma modules is given, and the existence of subsingular vectors is demonstrated. Free field realization of GW(3)(c(L),c(M)) and its highest weight modules are obtained within a rank 4 lattice VOA. Published under an exclusive license by AIP Publishing.