The Schrödinger group in d spatial dimensions can be embedded into relativistic conformal group in d + 1 dimensions SO(2, d + 2). This embedding is connected with the fact that one can get the Schrödinger equation from the massless Klein–Gordon equation through Kaluza–Klein compactification along null-like dimensions and Bargmann lift of Newton–Cartan theory. This embedding can also be viewed as the extension of the Schrödinger algebra to the maximal parabolic sub-algebra of SO(2, d + 2).