LATTICE ANALOGS OF W-ALGEBRAS AND CLASSICAL INTEGRABLE EQUATIONS

We propose a regular way to construct lattice versions of W-algebras, both for the quantum and the classical case. In the classical case we write the algebra explicitly and derive the lattice analogue of the Bo ussinesq equation from the Hamiltonian equations of motion. The connec tion between the lattice Faddeev-Takhtadjan-Volkov algebra and the q-d eformed Virasoro algebra is also discussed.