{"paper":{"title":"Construction of Simple Modules over the Quantum Affine Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Sanu Bera, Snehashis Mukherjee","submitted_at":"2020-01-21T10:31:20Z","abstract_excerpt":"The coordinate ring $\\mathcal{O}_{\\mathbf{q}}(\\mathbb{K}^n)$ of quantum affine space is the $\\mathbb{K}$-algebra presented by generators $x_1,\\cdots ,x_n$ and relations $x_ix_j=q_{ij}x_jx_i$ for all $i,j$. We construct simple $\\mathcal{O}_{\\mathbf{q}}(\\mathbb{K}^n)$-modules in a more general setting where the entries $q_{ij}$ lie in a torsion subgroup of $\\mathbb{K}^*$ and show analogous results hold as in single parameter case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.07432","kind":"arxiv","version":2},"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/2001.07432/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"}