  Sped-up protocols (shortcuts to adiabaticity) that drive a system quickly to
the same populations than a slow adiabatic process may involve Hamiltonian
terms difficult to realize in practice. We use the dynamical symmetry of the
Hamiltonian to find, by means of Lie transforms, alternative Hamiltonians that
achieve the same goals without the problematic terms. We apply this technique
to three-level systems (two interacting bosons in a double well, and beam
splitters with two and three output channels) driven by Hamiltonians that
belong to the four-dimensional algebra U3S3.
