We present Feigin's construction [Lectures given in Landau Institute] of lattice W algebras and give some simple results: lattice Virasoro and W 3 algebras. For the simplest case g=sl(2), we introduce the whole U q(2)) quantum group on this lattice. We find the simplest two-dimensional module as well as the exchange relations and define the lattice Virasoro algebra as the algebra of invariants of U q( sl(2)). Another generalization is connected with the lattice integrals of motion as the invariants of the quantum affine group U q(ñ+). We show that Volkov's scheme leads to a system of difference equations for a function of non-commutative variables.