{"paper":{"title":"The planar algebra of a coaction","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Teodor Banica","submitted_at":"2002-07-03T12:58:41Z","abstract_excerpt":"We study actions of ``compact quantum groups'' on ``finite quantum spaces''. According to Woronowicz and to general $\\c^*$-algebra philosophy these correspond to certain coactions $v:A\\to A\\otimes H$. Here $A$ is a finite dimensional $\\c^*$-algebra, and $H$ is a certain special type of Hopf *-algebra. If $v$ preserves a positive linear form $\\phi :A\\to\\c$, a version of Jones' ``basic construction'' applies. This produces a certain $\\c^*$-algebra structure on $A^{\\otimes n}$, plus a coaction $v_n :A^{\\otimes n}\\to A^{\\otimes n}\\otimes H$, for every $n$. The elements $x$ satisfying $v_n(x)=x\\oti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0207035","kind":"arxiv","version":3},"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"}