{"paper":{"title":"Weak Multiplier Hopf Algebras. The main theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Alfons Van Daele, Shuanhong Wang","submitted_at":"2012-10-16T13:15:36Z","abstract_excerpt":"A weak multiplier Hopf algebra is a pair (A,\\Delta) of a non-degenerate idempotent algebra A and a coproduct $\\Delta$ on A. The coproduct is a coassociative homomorphism from A to the multiplier algebra M(A\\otimes A) with some natural extra properties (like the existence of a counit). Further we impose extra but natural conditions on the ranges and the kernels of the canonical maps T_1 and T_2 defined from A\\otimes A to M(A\\otimes A) by T_1(a\\otimes b)=\\Delta(a)(1\\otimes b) and T_2(a\\ot b)=(a\\otimes 1)\\Delta(b).\n  The first condition is about the ranges of these maps. It is assumed that there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4395","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"}