Geodesic
Poisson reduction of the lattice Kac–Moody algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 2, pp. 179-187 
G. E. Arutyunov; P. B. Medvedev. Poisson reduction of the lattice Kac–Moody algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 2, pp. 179-187. http://geodesic.mathdoc.fr/item/TMF_1996_107_2_a0/
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     title = {Poisson reduction of the lattice {Kac{\textendash}Moody} algebra},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The poisson reduction of the $SL(N)$ lattice Kac–Moody algebra under the action of the maximal nilpotent subgroup of $SL(N)$ is considered. Poisson brackets on the reduced phase space are constructed. For $N=2$ in the continuous limit they comprise with the Gelfand–Fuchs cocycle.

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