{"paper":{"title":"Generalized (co)integrals on coideal subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Pawe{\\l} Kasprzak","submitted_at":"2018-10-16T16:13:23Z","abstract_excerpt":"Given a a Hopf algebra $H$, its left coideal subalgebra $A$ and a non-zero multiplicative functional $\\mu$ on $A$, we define the space of left $\\mu$-integrals $L^A_\\mu\\subset A$. We observe that $\\dim L^A_\\mu=1$ if $A$ is a Frobenius algebra and we conclude this equality for finite dimensional left coideal subalgebras of a weakly finite Hopf algebra. In general we prove that if $\\dim L^A_\\mu>0$ then $\\dim A <\\infty$. Given a group-like element $g\\in H$ we define the space $L^g_{ A}\\subset A'$ of $g$-cointegrals on $ A$ and linking this concept with the theory of $\\mu$-integrals we observe that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07114","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"}