Hidden symmetries and their group structure for some two-dimensional models

Two-dimensional classical relativistically invariant integrable (admitting infinitely many conservation laws) field-theory models are considered. It is shown that the local conserved currents for the Thirring model, the higher energy-momentum tensors for the sigma models, the sine-Gordon and Liouville systems, and some nonlocal conserved currents for the sigma models (including the supersymmetric case) have a Noether character. The corresponding symmetries are usually said to be hidden, because they are not imposed in the construction of the model. The explicit form of the hidden symmetry transformations is found for the listed models. For the sigma models, the Thirring model, and all conformally invariant two-dimensional models transformations whose generators form an infinite-dimensional closed algebra are also identified