Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras
Author(s)De Sole, Alberto; Valeri, Daniele; Kac, Victor
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We describe of the generalized 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in Mathematical Physics
De Sole, Alberto, Victor G. Kac, and Daniele Valeri. “Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras.” Commun. Math. Phys. 323, no. 2 (August 22, 2013): 663–711.
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