01065nas a2200133   4500008004100000245012700041210006900168260001300237520058400250100002100834700002000855700002000875856003600895       2013                        en  d00aClassical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian  systems within the theory of Poisson vertex algebras0 aClassical Walgebras and generalized DrinfeldSokolov biHamiltonia  bSpringer3 aWe 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.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele  uhttp://hdl.handle.net/1963/6978