{"paper":{"title":"An algebraic theory for logarithmic Kazhdan-Lusztig correspondences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.RT"],"primary_cat":"math.QA","authors_text":"Matthew Rupert, Simon Lentner, Thomas Creutzig","submitted_at":"2023-06-20T12:25:51Z","abstract_excerpt":"Let $\\mathcal{U}$ be a braided tensor category, typically unknown, complicated and in particular non-semisimple. We characterize $\\mathcal{U}$ under the assumption that there exists a commutative algebra $A$ in $\\mathcal{U}$ with certain properties: Let $\\mathcal{C}$ be the category of local $A$-modules in $\\mathcal{U}$ and $\\mathcal{B}$ the category of $A$-modules in $\\mathcal{U}$, which are in our set-up usually much simpler categories than $\\mathcal{U}$. Then we can characterize $\\mathcal{U}$ as a relative Drinfeld center $\\mathcal{Z}_\\mathcal{C}(\\mathcal{B})$ and $\\mathcal{B}$ as represent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11492","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/2306.11492/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"}