{"paper":{"title":"Algebraic quantum groupoids - An example","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alfons Van Daele","submitted_at":"2017-02-16T09:50:13Z","abstract_excerpt":"Let $B$ and $C$ be non-degenerate idempotent algebras and assume that $E$ is a regular separability idempotent in $M(B\\otimes C)$. Define $A=C\\otimes B$ and $\\Delta:A\\to M(A\\otimes A)$ by $\\Delta(c\\otimes b)=c\\otimes E\\otimes b$. The pair $(A,\\Delta)$ is a weak multiplier Hopf algebra. Because we assume that $E$ is regular, it is a regular weak multiplier Hopf algebra. There is a faithful left integral on $(A,\\Delta)$ that is also right invariant. Therefore, we call $(A,\\Delta)$ a unimodular algebraic quantum groupoid. By the general theory, the dual $(\\widehat A,\\widehat \\Delta)$ can be const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04903","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"}