{"paper":{"title":"Hopf Algebras which Factorize through the Taft Algebra $T_{m^{2}}(q)$ and the Group Hopf Algebra $K[C_{n}]$","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Ana-Loredana Agore","submitted_at":"2016-11-17T13:30:53Z","abstract_excerpt":"We completely describe by generators and relations and classify all Hopf algebras which factorize through the Taft algebra $T_{m^{2}}(q)$ and the group Hopf algebra $K[C_{n}]$: they are $nm^{2}$-dimensional quantum groups $T_{nm^{2}}^ {\\omega}(q)$ associated to an $n$-th root of unity $\\omega$. Furthermore, using Dirichlet's prime number theorem we are able to count the number of isomorphism types of such Hopf algebras. More precisely, if $d = {\\rm gcd}(m,\\nu(n))$ and $\\frac{\\nu(n)}{d} = p_1^{\\alpha_1} \\cdots p_r^{\\alpha_r}$ is the prime decomposition of $\\frac{\\nu(n)}{d}$ then the number of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05674","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"}