%0 Journal Article %J Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 %D 2013 %T Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X 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. %B Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 %I Springer %G en %U http://hdl.handle.net/1963/6978 %1 6966 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2013-07-13T15:24:57Z No. of bitstreams: 1 1207.6286v3.pdf: 588052 bytes, checksum: a5630eb1399cba992d56be98f25cdc9c (MD5) %R 10.1007/s00220-013-1785-z