Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
| dc.contributor.area | Mathematics | en_US |
| 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.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.identifier.uri | https://openscience.sissa.it/handle/1963/7242 | |
| dc.language.iso | en | en_US |
| dc.miur.area | -1 | 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 |