{"paper":{"title":"Dimension and Trace of the Kauffman Bracket Skein Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Charles Frohman, Joanna Kania-Bartoszynska, Thang Le","submitted_at":"2019-02-06T02:13:37Z","abstract_excerpt":"Let $F$ be a finite type surface and $\\zeta$ a complex root of unity. The Kauffman bracket skein algebra $K_{\\zeta}(F)$ is an important object in both classical and quantum topology as it has relations to the character variety, the Teichm\\\"uller space, the Jones polynomial, and the Witten-Reshetikhin-Turaev Topological Quantum Field Theories. We compute the rank and trace of $K_{\\zeta}(F)$ over its center, and we extend a theorem of Frohman and Kania-Bartoszynska which says the skein algebra has a splitting coming from two pants decompositions of $F$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02002","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":""},"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"}