{"paper":{"title":"Koszul duality in deformation quantization, I","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Boris Shoikhet","submitted_at":"2007-06-15T22:27:59Z","abstract_excerpt":"Let $\\alpha$ be a polynomial Poisson bivector on a finite-dimensional vector space $V$ over $\\mathbb{C}$. Then Kontsevich [K97] gives a formula for a quantization $f\\star g$ of the algebra $S(V)^*$. We give a construction of an algebra with the PBW property defined from $\\alpha$ by generators and relations. Namely, we define an algebra as the quotient of the free tensor algebra $T(V^*)$ by relations $x_i\\otimes x_j-x_j\\otimes x_i=R_{ij}(\\hbar)$ where $R_{ij}(\\hbar)\\in T(V^*)\\otimes\\hbar \\mathbb{C}[[\\hbar]]$, $R_{ij}=\\hbar \\Sym(\\alpha_{ij})+\\mathcal{O}(\\hbar^2)$, with one relation for each pair"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2381","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0706.2381/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}