  We represent Feigin's construction [11] of lattice W algebras and give some
simple results: lattice Virasoro and $W_3$ algebras. For simplest case
$g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We
find simplest two-dimensional module as well as exchange relations and define
lattice Virasoro algebra as algebra of invariants of $U_q(sl(2))$. Another
generalization is connected with lattice integrals of motion as the invariants
of quantum affine group $U_q(\hat{n}_{+})$. We show that Volkov's scheme leads
to the system of difference equations for the function from non-commutative
variables.Continium limit of this lattice algebras are considered.
