{"paper":{"title":"The Localized Skein Algebra is Frobenius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Charles Frohman, Nel Abdiel","submitted_at":"2015-01-12T13:02:00Z","abstract_excerpt":"When $A$ in the Kauffman bracket skein relation is a primitive $2N$th root of unity, where $N\\geq 3$ is odd, the Kauffman bracket skein algebra $K_N(F)$ of a finite type surface $F$ is a ring extension of the $SL_2\\mathbb{C}$-characters $\\chi(F)$ of the fundamental group of $F$. We localize by inverting the nonzero characters to get an algebra $S^{-1}K_N(F)$ over the function field of the character variety. We prove that if $F$ is noncompact, the algebra $S^{-1}K_N(F)$ is a symmetric Frobenius algebra. Along the way we prove $K(F)$ is finitely generated, $K_N(F)$ is a finite rank module over $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02631","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"}