{"paper":{"title":"Compact and discrete subgroups of algebraic quantum groups I","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.OA","authors_text":"A. Van Daele, M.B. Landstad","submitted_at":"2007-02-15T16:03:35Z","abstract_excerpt":"Let $G$ be a locally compact group. Consider the C$^*$-algebra $C_0(G)$ of continuous complex functions on $G$, tending to 0 at infinity. The product in $G$ gives rise to a coproduct $\\Delta_G$ on the C$^*$-algebra $C_0(G)$. A locally compact {\\it quantum} group is a pair $(A,\\Delta)$ of a C$^*$-algebra $A$ with a coproduct $\\Delta$ on $A$, satisfying certain conditions. The definition guarantees that the pair $(C_0(G),\\Delta_G)$ is a locally compact quantum group and that conversely, every locally compact quantum group $(A,\\Delta)$ is of this form when the underlying C$^*$-algebra $A$ is abel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702458","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0702458/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"}