Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras
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Kac_Classical w-algebras.pdf
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Author(s)
De Sole, Alberto
Valeri, Daniele
Kac, Victor
Date Issued
August 2013
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
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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Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00220-013-1785-z
