Geodesic
Poisson reduction of the lattice Kac--Moody algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 2, pp. 179-187

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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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     author = {G. E. Arutyunov and P. B. Medvedev},
     title = {Poisson reduction of the lattice {Kac--Moody} algebra},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {2},
     year = {1996},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1996_107_2_a0/}
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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/