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 |
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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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