TY - RPRT T1 - Structure of classical (finite and affine) W-algebras Y1 - 2014 A1 - Alberto De Sole A1 - Victor G. Kac A1 - Daniele Valeri AB - First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W-algebra W(g,f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W^{fin}(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras. PB - SISSA UR - http://hdl.handle.net/1963/7314 N1 - 40 pages U1 - 7359 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER -