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Lattice $W$ algebras and quantum groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 132-147 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $U_q(sl(2))$ 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 $U_q(\hat {n}_{+})$. We show that Volkov's scheme leads to a system of difference equations for a function of non-commutative variables. 
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Ya. P. Pugay. Lattice $W$ algebras and quantum groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 132-147. http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a12/

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