  We propose a mechanism to suppress heating in periodically driven many-body
quantum systems by employing sufficiently long-range interactions and
experimentally relevant initial conditions. The mechanism is robust to local
perturbations and does \emph{not} rely on disorder or high driving frequencies.
Instead, it makes use of an approximate fragmentation of the many-body spectrum
of the non-driven system into bands, with band gaps that grow with the system
size. We show that when these systems are driven, there is a regime where
\emph{decreasing} the driving frequency \emph{decreases} heating and
entanglement build-up. This is demonstrated numerically for a prototypical
system of spins in one dimension, but the results can be readily generalized to
higher dimensions.
