{"paper":{"title":"On semisimple Hopf algebras of dimension $2^{m}$, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yevgenia Kashina","submitted_at":"2015-10-09T12:13:00Z","abstract_excerpt":"In this paper we classify, up to equivalence, all semisimple nontrivial Hopf algebras of dimension $2^{2n+1}$ for $n\\geq 2$ over an algebraically closed field of characteristic $0$ with the group of group-like elements isomorphic to $\\mathbb{Z}_{2^{n}}\\times \\mathbb{Z}_{2^{n}}$. Moreover we classify all such nonisomorphic Hopf algebras of dimension $32$ and show that they are not twist-equivalent to each other. More generally, given an abelian group of order $2^{m-1}$ we give an upper bound for the number of nonisomorphic nontrivial Hopf algebras of dimension $2^{m}$ which have this group as t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02645","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"}