Classical W-algebras within the theory of Poisson vertex algebras

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)

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
• 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