{"paper":{"title":"A Wiener Lemma for the discrete Heisenberg group: Invertibility criteria and applications to algebraic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RT"],"primary_cat":"math.DS","authors_text":"Evgeny Verbitskiy, Klaus Schmidt, Martin G\\\"oll","submitted_at":"2016-03-27T15:18:56Z","abstract_excerpt":"This article contains a Wiener Lemma for the convolution algebra $\\ell^1(\\mathbb H,\\mathbb C)$ and group $C^\\ast$-algebra $C^\\ast(\\mathbb H)$ of the discrete Heisenberg group $\\mathbb H$. At first, a short review of Wiener's Lemma in its classical form and general results about invertibility in group algebras of nilpotent groups will be presented. The known literature on this topic suggests that invertibility investigations in the group algebras of $\\mathbb H$ rely on the complete knowledge of $\\widehat{\\mathbb H}$ -- the dual of $\\mathbb H$, i.e., the space of unitary equivalence classes of i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08225","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"}