{"paper":{"title":"Quantum traces for $SL_n$-skein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Tao Yu, Thang T. Q. L\\^e","submitted_at":"2023-03-14T17:13:15Z","abstract_excerpt":"We establish the existence of several quantum trace maps. The simplest one is an algebra map between two quantizations of the algebra of regular functions on the $SL_n$-character variety of a surface $\\mathfrak{S}$ equipped with an ideal triangulation $\\lambda$. The first is the (stated) $SL_n$-skein algebra $\\mathscr{S}(\\mathfrak{S})$. The second $\\overline{\\mathcal{X}}(\\mathfrak{S},\\lambda)$ is the Fock and Goncharov's quantization of their $X$-moduli space. The quantum trace is an algebra homomorphism $\\bar{tr}^X:\\overline{\\mathscr{S}}(\\mathfrak{S})\\to\\overline{\\mathcal{X}}(\\mathfrak{S},\\la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.08082","kind":"arxiv","version":2},"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/2303.08082/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"}