{"paper":{"title":"Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Jun Tomiyama, Marcel de Jeu","submitted_at":"2014-07-31T09:31:15Z","abstract_excerpt":"If $X$ is a compact Hausdorff space and $\\sigma$ is a homeomorphism of $X$, then a Banach algebra $\\ell^1(\\Sigma)$ of crossed product type is naturally associated with this topological dynamical system $\\Sigma=(X,\\sigma)$. If $X$ consists of one point, then $\\ell^1(\\Sigma)$ is the group algebra of the integers.\n  We study the algebraically irreducible representations of $\\ell^1(\\Sigma)$ on complex vector spaces, its primitive ideals and its structure space. The finite dimensional algebraically irreducible representations are determined up to algebraic equivalence, and a sufficiently rich famil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8328","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"}