{"paper":{"title":"$U_q^+(B_2)$ and its representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Sanu Bera, Snehashis Mukherjee","submitted_at":"2025-03-27T05:44:45Z","abstract_excerpt":"In this article we investigate the algebra $U_q^+(B_2)$. Assume that $q$ is a primitive $m$-th root of unity with $m \\geq 5$. We prove that $U_q^+(B_2)$ becomes a Polynomial Identity (PI) algebra. It was previously known that for such algebras the simple modules are finite-dimensional with dimension at most the PI degree. We determine the PI degree of $U_q^+(B_2)$ and we classify up to isomorphism the simple $U_q^+(B_2)$-modules. We also find the center of $U_q^+(B_2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21170","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.21170/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}