  The maximal algebra of symmetries of the free single-particle Schroedinger
equation is determined and its relevance for the holographic duality in
non-relativistic Fermi systems is investigated. This algebra of symmetries is
an infinite dimensional extension of the Schroedinger algebra, it is isomorphic
to the Weyl algebra of quantum observables, and it may be interpreted as a
non-relativistic higher-spin algebra. The associated infinite collection of
Noether currents bilinear in the fermions are derived from their relativistic
counterparts via a light-like dimensional reduction. The minimal coupling of
these currents to background sources is rewritten in a compact way by making
use of Weyl quantisation. Pushing forward the similarities with the holographic
correspondence between the minimal higher-spin gravity and the critical O(N)
model, a putative bulk dual of the unitary and the ideal Fermi gases is
discussed.
