1207.6286 (Alberto De Sole et al.)

Classical W-algebras and Drinfeld-Sokolov bi-Hamiltonian systems within
the theory of Poisson vertex algebras    [PDF]

Alberto De Sole, Victor G. Kac, Daniele Valeri

We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical 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.

View original: http://arxiv.org/abs/1207.6286