{"paper":{"title":"Heisenberg duoble, pentagon equation, structure and classification of finite dimensional Hopf algebras","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"G. Militaru","submitted_at":"2000-09-14T08:11:16Z","abstract_excerpt":"The study of the pentagon (fusion) equation leds to the Structure and the Classification theorem for finite dimenasional Hopf algebras: there exists a one to one correspondence between the set of types of n-dimensional Hopf algebtras and the set of the orbits of the resticted Jordan action $GL_n(k) \\times M_n(k)\\otimes M_n(k) \\to M_n(k) \\otimes M_nk$ $(u, R) \\to (u\\otimes u)R (u\\otimes u)^{-1}$, the representatives of wich are invertible solutions of length n of the pentagon equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009141","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"}