{"paper":{"title":"Sandwich classification for $GL_n(R)$, $O_{2n}(R)$ and $U_{2n}(R,\\Lambda)$ revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Raimund Preusser","submitted_at":"2017-05-05T23:02:19Z","abstract_excerpt":"Let $n$ be a natural number greater or equal to $3$, $R$ a commutative ring and $\\sigma\\in GL_n(R)$. We show that $t_{kl}(\\sigma_{ij})$ (resp. $t_{kl}(\\sigma_{ii}-\\sigma_{jj}))$ where $i\\neq j$ and $k\\neq l$ can be expressed as a product of $8$ (resp. $24$) matrices of the form $^{\\epsilon}\\sigma^{\\pm 1}$ where $\\epsilon\\in E_n(R)$. We prove similar results for the orthogonal groups $O_{2n}(R)$ and the hyperbolic unitary groups $U_{2n}(R,\\Lambda)$ under the assumption that $R$ is commutative and $n\\geq 3$. This yields new, very short proofs of the Sandwich Classification Theorems for the group"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02415","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":""},"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"}