{"paper":{"title":"Combinatorics of graded module categories over skew polynomial algebras at roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.RA","authors_text":"Akihiro Higashitani, Kenta Ueyama","submitted_at":"2024-09-17T05:46:57Z","abstract_excerpt":"We introduce an operation on skew-symmetric matrices over $\\mathbb{Z}/\\ell\\mathbb{Z}$ called switching, and also define a class of skew-symmetric matrices over $\\mathbb{Z}/\\ell\\mathbb{Z}$ referred to as modular Eulerian matrices. We then show that these are closely related to the graded module categories over skew polynomial algebras at $\\ell$-th roots of unity. As an application, we study the point simplicial complexes of skew polynomial algebras at cube roots of unity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.10904","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/2409.10904/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"}