Abstract
In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket. In particular, we construct theW (l)n algebras, first discussed for the casen=3 andl=2 by Polyakov and Bershadsky.
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Communicated by N. Yu. Reshetikhin
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Burroughs, N.J., de Groot, M.F., Hollowood, T.J. et al. Generalized Drinfel'd-Sokolov hierarchies. Commun.Math. Phys. 153, 187–215 (1993). https://doi.org/10.1007/BF02099045
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DOI: https://doi.org/10.1007/BF02099045