{"paper":{"title":"On deformations of multidimensional Poisson brackets of hydrodynamic type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.DG","authors_text":"Matteo Casati","submitted_at":"2013-12-06T14:56:45Z","abstract_excerpt":"The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consists of a pair $(\\mathcal{A},\\{\\cdot_\\lambda\\cdot\\})$ of a differential algebra $\\mathcal{A}$ and a bilinear operation called the $\\lambda$-bracket. We extend the definition to the class of algebras $\\mathcal{A}$ endowed with $d\\geq1$ commuting derivations. We call this structure a \\emph{multidimensional PVA}: it is a suitable setting to study Hamiltonian PDEs with $d$ spatial dimensions. We apply this theory to the study of deformations of the Poisson brackets of hyd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1878","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}