Group structure of hidden symmetry transformations for supersymmetric nonlinear sigma models

The hidden symmetry transformations that generate via Noether's theorem conserved currents for two-dimensional supersymmetric nonlinear sigma models are considered. The group structure of these transformations is investigated, and it is shown that the generators with positive and with negative index (each separately) form infinite closed Lie algebras isomorphic to the algebra $\widetilde{\mathscr G}\otimes F(t)$ where $\widetilde{\mathscr G}$ is the Lie algebra of the subgroup $\widetilde G$, that leaves the initial data invariant and $F(t)$ is the class of rational functions. For the principal chiral superficial, it is shown that the maximal closed Lie algebra of the hidden symmetry transformations is isomorphic to the algebra $\mathscr G\otimes P(t,1/t)\oplus\mathscr G$, where $P(t, 1/t)$ are Laurent polynomials.