{"paper":{"title":"Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hui-Xiang Chen, Lan You, Zhen Wang","submitted_at":"2013-09-28T09:01:24Z","abstract_excerpt":"In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let $H=kG(\\chi, a,\\d)$ be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\\chi$ is a $k$-valued character for $G$ with $\\chi(a)\\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7442","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"}