Perfect fluid coupled to a solenoidal field which enjoys the l-conformal Galilei symmetry

A non-relativistic (Galilei-invariant) model of a perfect fluid coupled to a solenoidal field in arbitrary spatial dimension is considered. It contains an arbitrary parameter kappa and in the particular case of kappa = 1 it describes a perfect fluid coupled to a magnetic field. For a special value of kappa, the theory admits the Schrodinger symmetry group which is consistent with the magnetic case in two spatial dimensions only. Generalization to the case of the l-conformal Galilei group for an arbitrary half-integer parameter l is constructed.