Classical $${\mathcal{W}}$$W -Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras
@article{DeSole2012Classical, title={Classical \$\$\{\mathcal\{W\}\}\$\$W -Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras}, author={Alberto De Sole and Victor G. Kac and Daniele Valeri}, journal={Communications in Mathematical Physics}, year={2012}, volume={323}, pages={663-711} }
We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical $${\mathcal{W}}$$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…
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