{"paper":{"title":"Dynamical systems and operator algebras associated to Artin's representation of braid groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Tron Omland","submitted_at":"2016-09-15T17:06:08Z","abstract_excerpt":"Artin's representation is an injective homomorphism from the braid group $B_n$ on $n$ strands into $\\operatorname{Aut}\\mathbb{F}_n$, the automorphism group of the free group $\\mathbb{F}_n$ on $n$ generators. The representation induces maps $B_n\\to\\operatorname{Aut}C^*_r(\\mathbb{F}_n)$ and $B_n\\to\\operatorname{Aut}C^*(\\mathbb{F}_n)$ into the automorphism groups of the corresponding group $C^*$-algebras of $\\mathbb{F}_n$. These maps also have natural restrictions to the pure braid group $P_n$. In this paper, we consider twisted versions of the actions by cocycles with values in the circle, and d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04737","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"}