{"paper":{"title":"Triangular and Unitriangular Factorization of Twisted Chevalley Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.GR","authors_text":"Deep H. Makadiya, Shripad M. Garge","submitted_at":"2025-05-26T17:06:22Z","abstract_excerpt":"The existence of triangular and unitriangular factorizations has been extensively studied for untwisted Chevalley groups, as well as for twisted Chevalley groups of types other than ${}^2A_{2n} \\ (n \\geq 1)$. However, the case of twisted Chevalley groups of type ${}^2A_{2n} \\ (n \\geq 1)$, has remained unresolved in the general setting of commutative rings. Prior work by A. Smolensky addressed this case only over certain fields, including finite fields and the field of complex numbers. These results indicate that, even over fields, the ${}^2A_{2n}$ case demands more refined techniques, reflecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.20224","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/2505.20224/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"}