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Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras

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dc.contributor.author De Sole, Alberto
dc.contributor.author Kac, Victor G.
dc.contributor.author Valeri, Daniele
dc.date.accessioned 2014-01-10T07:39:17Z
dc.date.available 2014-01-10T07:39:17Z
dc.date.issued 2014-01-09
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/7242
dc.description 45 pages en_US
dc.description.abstract We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries arXiv:1401.2082;
dc.title Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras en_US
dc.type Preprint en_US
dc.miur.area -1 en_US
dc.contributor.area Mathematics en_US


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