Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras

De Sole, A., Kac, V. G. and Valeri, D. (2013) Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Communications in Mathematical Physics, 323(2), pp. 663-711. (doi: 10.1007/s00220-013-1785-z)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Valeri, Dr Daniele
Authors: De Sole, A., Kac, V. G., and Valeri, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
Publisher:Springer
ISSN:0010-3616
ISSN (Online):1432-0916
Published Online:22 August 2013

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