{"paper":{"title":"Relative Hom-Hopf modules and total integrals","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Shengxiang Wang, Shuangjian Guo, Xiaohui Zhang","submitted_at":"2014-11-26T12:30:33Z","abstract_excerpt":"Let $(H, \\a)$ be a monoidal Hom-Hopf algebra and $(A, \\b)$ a right $(H, \\a)$-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of $(A, \\b)$ in the setting of monoidal Hom-Hopf algebras. Also we prove that there exists a total integral $\\phi: (H, \\a)\\rightarrow (A, \\b)$ if and only if any representation of the pair $(H,A)$ is injective in a functorial way, as a corepresentation of $(H, \\a)$, which generalizes Doi's result. Finally, we define a total quantum integral $\\g: H\\rightarrow Hom(H, A)$ and prove the following affineness criterion: if there e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7205","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"}