{"paper":{"title":"On the Kontsevich $\\star$-product associativity mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","nlin.SI"],"primary_cat":"math.QA","authors_text":"Arthemy V. Kiselev, Ricardo Buring","submitted_at":"2016-02-29T16:40:29Z","abstract_excerpt":"The deformation quantization by Kontsevich [arXiv:q-alg/9709040] is a way to construct an associative noncommutative star-product $\\star=\\times+\\hbar \\{\\ ,\\ \\}_{P}+\\bar{o}(\\hbar)$ in the algebra of formal power series in $\\hbar$ on a given finite-dimensional affine Poisson manifold: here $\\times$ is the usual multiplication, $\\{\\ ,\\ \\}_{P}\\neq0$ is the Poisson bracket, and $\\hbar$ is the deformation parameter. The product $\\star$ is assembled at all powers $\\hbar^{k\\geq0}$ via summation over a certain set of weighted graphs with $k+2$ vertices; for each $k>0$, every such graph connects the two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09036","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"}