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Communications in Mathematical Physics

, Volume 323, Issue 2, pp 663–711 | Cite as

Classical \({\mathcal{W}}\) -Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras

  • Alberto De SoleEmail author
  • Victor G. Kac
  • Daniele Valeri
Article

Abstract

We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical \({\mathcal{W}}\) -algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.

Keywords

Poisson Structure Hamiltonian Equation Conformal Weight Differential Algebra Isotropic Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alberto De Sole
    • 1
    Email author
  • Victor G. Kac
    • 2
  • Daniele Valeri
    • 3
  1. 1.Dept. of Math.Univ. of Rome 1RomaItaly
  2. 2.Dept. of Math.MITCambridgeUSA
  3. 3.SISSA-ISASTriesteItaly

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