Generalized Drinfeld-Sokolov hierarchies 2: The Hamiltonian structures

Jun, 1991
41 pages
Published in:
  • Commun.Math.Phys. 153 (1993) 187-215
e-Print:
Report number:
  • IASSNS-HEP-91-42,
  • PUPT-1263

Citations per year

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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 Wn lW_n~l algebras, first discussed for the case n=3n=3 and l=2l=2 by A. Polyakov and M. Bershadsky.
Note:
  • 41 pages
  • Korteweg-de Vries equation
  • Hamiltonian formalism
  • algebra: Kac-Moody
  • transformation: gauge
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