{"paper":{"title":"Yoga of Commutators in Roy's Elementary Orthogonal Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.AC","authors_text":"A. A. Ambily","submitted_at":"2013-05-13T16:15:48Z","abstract_excerpt":"In this article, we give explicit proofs of certain commutator relations among the elementary generators of the elementary orthogonal group $EO_A(Q\\perp H(P))$, where $A$ is a commutative ring, $Q$ is a non-singular quadratic $A$-space and $H(P)$ is the hyperbolic space of a finitely generated projective module $P$ with the natural quadratic form. Using these relations, we established a local-global principle of D. Quillen for the Dickson--Siegel--Eichler--Roy (DSER) elementary orthogonal transformations in \\cite{aarr}. In \\cite{aa1}, by using these commutator relations, we prove the normality"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2826","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":""},"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"}