{"paper":{"title":"Diagonal reduction algebra for $\\mathfrak{osp}(1|2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Dwight Anderson Williams II, Jonas T. Hartwig","submitted_at":"2021-06-06T21:05:42Z","abstract_excerpt":"The problem of providing complete presentations of reduction algebras associated to a pair of Lie algebras $(\\mathfrak{G},\\mathfrak{g})$ has previously been considered by Khoroshkin and Ogievetsky in the case of the diagonal reduction algebra for $\\mathfrak{gl}(n)$. In this paper we consider the diagonal reduction algebra of the pair of Lie superalgebras $\\left(\\mathfrak{osp}(1|2) \\times \\mathfrak{osp}(1|2), \\mathfrak{osp}(1|2)\\right)$ as a double coset space having an associative diamond product and give a complete presentation in terms of generators and relations. We also provide a PBW basis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04380","kind":"arxiv","version":4},"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/2106.04380/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"}