OFF-CRITICAL CURRENT-ALGEBRAS

We discuss the infinite-dimensional algebras appearing in integrable p erturbations of conformally invariant theories, with special emphasis on the structure of the consequent non-Abelian infinite-dimensional al gebra generalizing W-infinity to the case of a non-Abelian group. We p rove that the pure left sector as well as the pure right sector of the thus-obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seem s to be near to being unraveled. We also find some subalgebras that co rrespond to Kac-Moody algebras. The constraints imposed by the algebra s are very strong and, in the case of the massive deformation of a non -Abelian fermionic model, the symmetry alone is enough to fix the two- and three-point functions of the theory.