Geodesic
Lattice $W$ algebras and quantum groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 132-147

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_1994_100_1_a12,
     author = {Ya. P. Pugay},
     title = {Lattice $W$ algebras and quantum groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {132--147},
     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a12/}
}
TY  - JOUR
AU  - Ya. P. Pugay
TI  - Lattice $W$ algebras and quantum groups
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 132
EP  - 147
VL  - 100
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a12/
LA  - ru
ID  - TMF_1994_100_1_a12
ER  - 
%0 Journal Article
%A Ya. P. Pugay
%T Lattice $W$ algebras and quantum groups
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 132-147
%V 100
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a12/
%G ru
%F TMF_1994_100_1_a12
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/