# 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}
}
• Published 26 July 2012
• Mathematics
• Communications in Mathematical Physics
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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We produce explicit generators of the classical $${\mathcal{W}}$$W-algebras associated with the principal nilpotents in the simple Lie algebras of all classical types and in the exceptional Lie
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We apply the new method for constructing integrable Hamiltonian hierarchies of Lax type equations developed in our previous paper to show that all $${\mathcal{W}}$$W-algebras
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