Valeri, D. (2014) Classical W-algebras within the theory of Poisson vertex algebras. In: Gorelik, M. and Papi, P. (eds.) Advances in Lie Superalgebras. Series: Springer INdAM series (7). Springer: Cham, pp. 203-221. ISBN 9783319029511 (doi: 10.1007/978-3-319-02952-8_12)
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Abstract
We review the Poisson vertex algebra theory approach to classical W-algebras. First, we provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras and we 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. Then we provide a Poisson vertex algebra analogue of the Gelfand-Dickey construction of classical W-algebras and we show the relations with the Drinfeld-Sokolov Hamiltonian reduction. It will be also shown that classical W-algebras are the Poisson vertex algebras which are of interest from the conformal field theory point of view.
Item Type: | Book Sections |
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Status: | Published |
Glasgow Author(s) Enlighten ID: | Valeri, Dr Daniele |
Authors: | Valeri, D. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Publisher: | Springer |
ISBN: | 9783319029511 |
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