{"paper":{"title":"Poisson algebras, Weyl algebras and Jacobi pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AC","math.AG","math.MP","math.RA"],"primary_cat":"math.QA","authors_text":"Yucai Su","submitted_at":"2011-07-06T12:55:42Z","abstract_excerpt":"We study Jacobi pairs in details and obtained some properties. We also study the natural Poisson algebra structure $(\\PP,[...,...],...)$ on the space $\\PP:=\\C[y]((x^{-\\frac1N}))$ for some sufficient large $N$, and introduce some automorphisms of $(\\PP,[...,...],...)$ which are (possibly infinite but well-defined) products of the automorphisms of forms $e^{\\ad_H}$ for $H\\in x^{1-\\frac1N}\\C[y][[x^{-\\frac1N}]]$ and $\\tau_c:(x,y)\\mapsto(x,y-cx^{-1})$ for some $c\\in\\C$. These automorphisms are used as tools to study Jacobi pairs in $\\PP$. In particular, starting from a Jacobi pair $(F,G)$ in $\\C[x,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1115","kind":"arxiv","version":9},"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"}