Abstract
Galilean W3 vertex operator algebra (VOA) GW3(cL,cM) 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 GW3(cL,cM) and its highest weight modules are obtained within a rank 4 lattice VOA.
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