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arXiv · hep-th/9109014

Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures

Nigel J. Burroughs·Mark F. deGroot·Timothy J. Hollowood·J. Luis Miramontes
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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 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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Nigel J. Burroughs, Mark F. deGroot, Timothy J. Hollowood, J. Luis Miramontes. 1991-09-10. Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures. https://doi.org/10.1007/bf02099045

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