{"paper":{"title":"Classification of PM Quiver Hopf Algebras","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Hui-Xiang Chen, Shouchuan Zhang, Yao-Zhong Zhang","submitted_at":"2004-10-06T11:14:56Z","abstract_excerpt":"We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field $k$ is the complex field and $G$ is a finite abelian group, we classify quiver Hopf algebras over $G$, multiple Taft algebras over $G$ and Nichols algebras in $^{kG}_{kG} {\\cal YD}$. We show that the quantum enveloping algebra of a complex semisimple Lie algebra is a quotient of a semi-path Hopf algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410150","kind":"arxiv","version":15},"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"}