Description
I will review physical properties of systems that have unusual non-local symmetries called Quantum Groups. I will focus on the case when the symmetry is fully internal, meaning that it commutes with the Hamiltonian, as well as with Lorentz transformations when they are present. We will find that in the continuum Quantum Group generically transforms local fields or operators into non-local ones, and acts naturally on defects present in the theory. We will then discuss non-integrable, chaotic, spin-chain systems and see that the symmetry has important consequences for both their low-energy behavior, as well as for high-temperature hydrodynamic regime.