{"paper":{"title":"Projective representations of almost unimodular groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Aldo Garcia Guinto","submitted_at":"2025-09-11T00:13:04Z","abstract_excerpt":"Given an almost unimodular $G$, so that the Plancherel weight $\\varphi_G$ on the group von Neumann algebra $L(G)$ is almost periodic, we show that the basic construction for the inclusion $L(G)^{\\varphi_G} \\leq L(G)$ is isomorphic to a twisted group von Neumann algebra of $G \\times \\Delta_G(G)\\hat{\\ }$ with a continuous 2-cocycle, where $\\Delta_G$ is the modular function. We show that when $G$ is second countable and admits a Borel 2-cocycle, $G$ is almost unimodular if and only if the central extension $\\mathbb{T} \\rtimes_{(1,\\omega)} G$ is almost unimodular. Using this result and the connect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09065","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.09065/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}