GENERALIZED DRINFELD-SOKOLOV HIERARCHIES .2. THE HAMILTONIAN STRUCTURES

Authors
BURROUGHS NJ DEGROOT MF HOLLOWOOD TJ MIRAMONTES JL
Citation
Nj. Burroughs et al., GENERALIZED DRINFELD-SOKOLOV HIERARCHIES .2. THE HAMILTONIAN STRUCTURES, Communications in Mathematical Physics, 153(1), 1993, pp. 187-215
Citations number
20
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
153
Issue
1
Year of publication
1993
Pages
187 - 215
Database
ISI
SICI code
0010-3616(1993)153:1<187:GDH.TH>2.0.ZU;2-3
Abstract
In this paper we examine the bi-Hamiltonian structure of the generaliz ed KdV-hierarchies. We verify that both Hamiltonian structures take th e form of Kirillov brackets on the Kac-Moody algebra, and that they de fine a coordinated system. Classical extended conformal algebras are o btained from the second Poisson bracket. In particular, we construct t he W(n)(l) algebras, first discussed for the case n = 3 and l = 2 by P olyakov and Bershadsky.