{"paper":{"title":"The Ore condition, affiliated operators, and the lamplighter group","license":"","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Peter Linnell (Virginia Tech), Thomas Schick (Goettingen), Wolfgang Lueck (Muenster)","submitted_at":"2002-02-04T16:20:33Z","abstract_excerpt":"Let G be the wreath product of Z and Z/2, the so called lamplighter group and k a commutative ring. We show that kG does not have a classical ring of quotients (i.e. does not satisfy the Ore condition). This answers a Kourovka notebook problem. Assume that kG is contained in a ring R in which the element 1-x is invertible, with x a generator of Z considered as subset of G. Then R is not flat over kG. If k is the field of complex numbers, this applies in particular to the algebra UG of unbounded operators affiliated to the group von Neumann algebra of G. We present two proofs of these results. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202027","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"}