{"paper":{"title":"Classification of certain inductive limit actions of compact groups on AF algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Qingyun Wang","submitted_at":"2016-08-13T14:25:49Z","abstract_excerpt":"Let $A=\\underrightarrow{\\lim}{A_n}$ be an AF algebra, $G$ be a compact group. We consider inductive limit actions of the form $\\alpha=\\underrightarrow{\\lim}{\\alpha_n}$, where $\\alpha_n\\colon G\\curvearrowright A_n$ is an action on the finite dimensional C*-algebra $A_n$ which fixes each matrix summand. If each $\\alpha_n$ is inner, such actions are classified by equivariant K-theory by Handelman and Rossmann. However, if the actions $\\alpha_n$ are not inner, we show that such actions are not classifiable by equivariant K-theory. We give a complete classification of such actions using twisted equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03986","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"}