{"paper":{"title":"The Freedman group: a physical interpretation for the SU(3)-subgroup D(18,1,1;2,1,1) of order 648","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.QA","authors_text":"Claire I. Levaillant","submitted_at":"2013-09-13T20:55:59Z","abstract_excerpt":"We study a subgroup $Fr(162\\times 4)$ of SU(3) of order 648 which is an extension of $D(9,1,1;2,1,1)$ and whose generators arise from anyonic systems. We show that this group is isomorphic to a semi-direct product $(\\mathbb{Z}/18\\mathbb{Z}\\times\\mathbb{Z}/6\\mathbb{Z})\\rtimes S_3$ with respect to conjugation and we give a presentation of the group. We show that the group $D(18,1,1;2,1,1)$ from the series $(D)$ in the existing classification for finite SU(3)-subgroups is also isomorphic to a semi-direct product $(\\mathbb{Z}/18\\mathbb{Z}\\times\\mathbb{Z}/6\\mathbb{Z})\\rtimes S_3$, also with respect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3580","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"}