On symplectic groups over polynomial rings

DOI10.1007/BF02571323zbMath0725.20038MaRDI QIDQ2277580

Fritz J. Grunewald, L.N.Vaserstein and E.R.Wheland, Jens Mennicke

Publication date: 1991

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174205

zbMATH Keywords

symplectic groupelementary matricespatchinglocalizationprincipal ideal domainLaurent polynomial ringprincipal ideal ringsymplectic symbolslocally principal ring

Mathematics Subject Classification ID

Group rings (16S34) Principal ideal rings (13F10) Other matrix groups over rings (20H25) Linear algebraic groups over adèles and other rings and schemes (20G35) Stability for linear groups (19B14)

Related Items

On the groups \(\mathrm{SL}_ 2(\mathbb{Z}[x)\) and \(\mathrm{SL}_ 2(k[x,y])\)] ⋮ Bounded reduction of orthogonal matrices over polynomial rings ⋮ Homotopy invariance of non-stable K₁-functors ⋮ Linear groups over general rings. I: Generalities. ⋮ Overgroups of elementary symplectic groups ⋮ Holomorphic factorization of mappings into \(\mathrm{Sp}_4 (\mathbb{C})\) ⋮ On homotopy invariance for homology of rank two groups. ⋮ Bounded reduction for Chevalley groups of types \(E_6\) and \(E_7\) ⋮ Property (𝑇) for Groups Graded by Root Systems ⋮ On presentations of integer polynomial points of simple groups over number fields. ⋮ Non-abelian \(K\)-theory for Chevalley groups over rings. ⋮ Clifford quantum cellular automata: Trivial group in 2D and Witt group in 3D ⋮ Elementary equivalence of Chevalley groups over fields. ⋮ ¹-Homotopy of Chevalley Groups ⋮ Local-global principle for congruence subgroups of Chevalley groups. ⋮ Chevalley groups of polynomial rings over Dedekind domains ⋮ Factorization of symplectic matrices into elementary factors ⋮ Chevalley groups over commutative rings. I: Elementary calculations ⋮ Subgroups of symplectic groups that contain a subsystem subgroup.

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