{"paper":{"title":"Multiple Commutator Formulas for Unitary Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Nikolai Vavilov, Roozbeh Hazrat, Zuhong Zhang","submitted_at":"2012-05-31T01:36:40Z","abstract_excerpt":"Let $(\\FormR)$ be a form ring such that $A$ is quasi-finite $R$-algebra (i.e., a direct limit of module finite algebras) with identity. We consider the hyperbolic Bak's unitary groups $\\GU(2n,\\FormR)$, $n\\ge 3$. For a form ideal $(I,\\Gamma)$ of the form ring $(\\FormR)$ we denote by $\\EU(2n,I,\\Gamma)$ and $\\GU(2n,I,\\Gamma)$ the relative elementary group and the principal congruence subgroup of level $(I,\\Gamma)$, respectively. Now, let $(I_i,\\Gamma_i) $, $i=0,...,m$, be form ideals of the form ring $(A,\\Lambda)$. The main result of the present paper is the following multiple commutator formula\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6866","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"}