{"paper":{"title":"Fullness of crossed products of factors by discrete groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Amine Marrakchi","submitted_at":"2018-11-17T01:29:13Z","abstract_excerpt":"Let $M$ be an arbitrary factor and $\\sigma : \\Gamma \\curvearrowright M$ an action of a discrete group. In this paper, we study the fullness of the crossed product $M \\rtimes_\\sigma \\Gamma$. When $\\Gamma$ is amenable, we obtain a complete characterization: the crossed product factor $M \\rtimes_\\sigma \\Gamma$ is full if and only if $M$ is full and the quotient map $\\overline{\\sigma} : \\Gamma \\rightarrow \\mathrm{Out}(M)$ has finite kernel and discrete image. This answers a question of Jones from 1981. When $M$ is full and $\\Gamma$ is arbitrary, we give a sufficient condition for $M \\rtimes_\\sigma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08274","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"}