{"paper":{"title":"Swapping algebra, Virasoro algebra and discrete integrable system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DG","authors_text":"Zhe Sun","submitted_at":"2014-12-14T09:38:49Z","abstract_excerpt":"We induce a Poisson algebra $\\{\\cdot,\\cdot\\}_{\\mathcal{C}_{n,N}}$ on the configuration space $\\mathcal{C}_{n,N}$ of $N$ twisted polygons in $\\mathbb{RP}^{n-1}$ from the swapping algebra \\cite{L12}, which is found coincide with Faddeev-Takhtajan-Volkov algebra for $n=2$. There is another Poisson algebra $\\{\\cdot,\\cdot\\}_{S2}$ on $\\mathcal{C}_{2,N}$ induced from the first Adler-Gelfand-Dickey Poissson algebra by Miura transformation. By observing that these two Poisson algebras are asymptotically related to the dual to the Virasoro algebra, finally, we prove that $\\{\\cdot,\\cdot\\}_{\\mathcal{C}_{2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4330","kind":"arxiv","version":3},"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"}