{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sandwich-classification-for-o-2n-1-r-and-u-2n","title":"Sandwich classification for $O_{2n+1}(R)$ and $U_{2n+1}(R,Δ)$ revisited","arxiv_id":"1801.00699","date":"2018-01-02","proceeding":null,"authors":["Raimund Preusser"],"abstract":"In a recent paper, the author proved that if $n\\geq 3$ is a natural number, $R$ a commutative ring and $\\sigma\\in GL_n(R)$, then $t_{kl}(\\sigma_{ij})$ where $i\\neq j$ and $k\\neq l$ can be expressed as a product of $8$ matrices of the form $^{\\epsilon}\\sigma^{\\pm 1}$ where $\\epsilon\\in E_n(R)$. In this article we prove similar results for the odd-dimensional orthogonal groups $O_{2n+1}(R)$ and the odd-dimensional unitary groups $U_{2n+1}(R,\\Delta)$ under the assumption that $R$ is commutative and $n\\geq 3$. This yields new, short proofs of the Sandwich Classification Theorems for the groups $O_{2n+1}(R)$ and $U_{2n+1}(R,\\Delta)$.","url_abs":"https://arxiv.org/abs/1801.00699v1","url_pdf":"https://arxiv.org/pdf/1801.00699v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"sandwich-classification-for-o-2n-1-r-and-u-2n","repo_url":"https://github.com/vpsg-research/waveguard","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}