Lattice analogues of W-algebras and classical integrable equations

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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 Boussinesq equation from the Hamiltonian equations of motion. The connection between the lattice Faddeev-Takhtadjan-Volkov algebra and the q-deformed Virasoro algebra is also discussed.