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

@article{DeSole2012Classical,
  title={Classical \$\$\{\mathcal\{W\}\}\$\$W -Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras},
  author={Alberto De Sole and Victor G. Kac and Daniele Valeri},
  journal={Communications in Mathematical Physics},
  year={2012},
  volume={323},
  pages={663-711}
}
We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical $${\mathcal{W}}$$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… 

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