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N=4 supersymmetric extensions of the l-conformal Galilei algebra areconstructed by properly extending the Lie superalgebra associated with the mostgeneral N=4 superconformal group in one dimension D(2,1;a). If the accelerationgenerators in the superalgebra form analogues of the irreducible (1,4,3)-,(2,4,2)-, (3,4,1)-, and (4,4,0)-supermultiplets of D(2,1;a), the parameter aturns out to be constrained by the Jacobi identities. In contrast, if the towerof the acceleration generators resembles a component decomposition of a genericreal superfield, which is a reducible representation of D(2,1;a), a remainsarbitrary. An N=4 l-conformal Galilei superalgebra recently proposed in [Phys.Lett. B 771 (2017) 401] is shown to be a particular instance of a more generalconstruction in this work.

N=4 l-conformal Galilei superalgebras inspired by D(2,1;a) supermultiplets