Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures

Details Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures

1991-09-10

arxiv.org/abs/hep-th/9109014v1

Commun.Math.Phys. 153 (1993) 187-215

Physics

High Energy Physics

High Energy Physics - Theory

41 pages

Scientific paper

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 the $W_n^l$ algebras, first discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.

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