{"paper":{"title":"The Classification of All Crossed Products $H_4 \\# k[C_{n}]$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Ana-Loredana Agore, Costel-Gabriel Bontea, Gigel Militaru","submitted_at":"2012-10-29T15:57:56Z","abstract_excerpt":"Using the computational approach introduced in [Agore A.L., Bontea C.G., Militaru G., J. Algebra Appl. 12 (2013), 1250227, 24 pages, arXiv:1207.0411] we classify all coalgebra split extensions of $H_4$ by $k[C_n]$, where $C_n$ is the cyclic group of order $n$ and $H_4$ is Sweedler's $4$-dimensional Hopf algebra. Equivalently, we classify all crossed products of Hopf algebras $H_4 \\# k[C_{n}]$ by explicitly computing two classifying objects: the cohomological 'group' ${\\mathcal H}^{2} ( k[C_{n}], H_4)$ and $\\text{CRP}( k[C_{n}], H_4):=$ the set of types of isomorphisms of all crossed products $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7700","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"}