{"paper":{"title":"The $SU(3)$ $A_1$ graph and its associated quantum groupoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Esteban Isasi, Luis V\\'asquez, Maria D\\'ias","submitted_at":"2018-12-20T18:01:28Z","abstract_excerpt":"An explicit and complete construction of the $SU(3)$ $A_1$ associated quantum groupoid is presented in this work, inspired by the approach taken by Trinchero for the $SU(2)$ $A_l$ graphs. New creation and annihilation operators were defined in order to consider the $3$ different types of back-tracks which appear due to the specific structure of $SU(3)$. The $C^{\\star}$ bialgebra and the realization of a Temperley-Lieb algebra is studied thoroughly. Finally, it is shown that the construction of the quantum groupoids associated to the $A_{1}$ $SU(N)$ graphs are easily obtained for any value of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08730","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"}