{"paper":{"title":"What is a double star-product?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Nikita Safonkin","submitted_at":"2025-05-31T20:13:24Z","abstract_excerpt":"Double Poisson brackets, introduced by M. Van den Bergh in 2004, are noncommutative analogs of the usual Poisson brackets in the sense of the Kontsevich-Rosenberg principle: they induce Poisson structures on the space of $N$-dimensional representations $\\operatorname{Rep}_N(A)$ of an associative algebra $A$ for any $N$. The problem of deformation quantization of double Poisson brackets was raised by D. Calaque in 2010, and had remained open since then.\n  In this paper, we address this problem by answering the question in the title. We present a structure on $A$ that induces a star-product unde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00699","kind":"arxiv","version":4},"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/2506.00699/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"}