Classical W-algebras within the theory of Poisson vertex algebras

@inproceedings{Sole2014ClassicalWW,
  title={Classical W-algebras within the theory of Poisson vertex algebras},
  author={Alberto De Sole and Victor G. Kac and Daniele Valeri},
  year={2014}
}
We review the Poisson vertex algebra theory approach to classical W-algebras. First, we provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras and we 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. Then we provide a Poisson vertex algebra… 

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