{"paper":{"title":"How to quantize the antibracket","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dimitry Leites (Stockholm University), Irina Shchepochkina (Independent University of Moscow)","submitted_at":"2005-10-12T16:46:07Z","abstract_excerpt":"The uniqueness of (the class of) deformation of Poisson Lie algebra has long been a completely accepted folklore.\n  Actually, it is wrong as stated, because its validity depends on the class of functions that generate Poisson Lie algebra, Po(2n): it is true for polynomials but false for Laurent polynomials.\n  We show that unlike the Lie superalgebra Po(2n|m), its quotient modulo center, the Lie superalgebra H(2n|m) of Hamiltonian vector fields with polynomial coefficients, has exceptional extra deformations for (2n|m)=(2|2) and only for this superdimension. We relate this result to the complet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510048","kind":"arxiv","version":1},"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"}