{"paper":{"title":"Serre Theorem for involutory Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"G. Militaru","submitted_at":"2009-06-13T14:04:47Z","abstract_excerpt":"We call a monoidal category ${\\mathcal C}$ a Serre category if for any $C$, $D \\in {\\mathcal C}$ such that $C\\ot D$ is semisimple, $C$ and $D$ are semisimple objects in ${\\mathcal C}$. Let $H$ be an involutory Hopf algebra, $M$, $N$ two $H$-(co)modules such that $M \\otimes N$ is (co)semisimple as a $H$-(co)module. If $N$ (resp. $M$) is a finitely generated projective $k$-module with invertible Hattory-Stallings rank in $k$ then $M$ (resp. $N$) is (co)semisimple as a $H$-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel'd modules over"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2479","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"}