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Generalized Drinfel'd-Sokolov hierarchies / Nigel J. Burroughs; Mark F. de Groot; J.Luis Miramontes; Timothy Hollowood

Communications in Mathematical Physics, Volume: "153", Issue: 1, Pages: 187 - 215

Swansea University Author: Timothy, Hollowood

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DOI (Published version): 10.1007/BF02099045

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 sec...

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Published in: Communications in Mathematical Physics
ISSN: 0010-3616 1432-0916
Published: 1991
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URI: https://cronfa.swan.ac.uk/Record/cronfa28598
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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.
College: College of Science
Issue: 1
Start Page: 187
End Page: 215