Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are...

A particular type of`resonant' periodic driving of a symmetric dynamical system may cause the time-one map of the driven system to have a non-trivial root that possesses less symmetry than the time-one map itself. The latter phenomenon is called k-symmetry. Some examples and consequences to the dynamical behaviour are pointed out brieey.