Overdiagonal subgroups of the hyperbolic unitary group for a good form ring over a field
type: Item
instance of: scholarly article
title: Overdiagonal subgroups of the hyperbolic unitary group for a good form ring over a field
zbMATH Open document ID: 0935.20042
DOI: 10.1007/BF02169965
author: E. V. Dybkova
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-10-05T00:00:00Z
review text: Let \((R,\Lambda)\) be a form ring over a field \(R\), \(R_0\) the subfield of \(R\) consisting of all elements fixed by the involution, and \(U(2n,R,\Lambda)\) the hyperbolic unitary group. The author proves that, if \(\text{card }R\geq 13\) and \(\text{card }R_0\geq 7\), then the lattice of subgroups of \(U(2n,R,\Lambda)\) that contain all diagonal unitary matrices allows the standard description except for the symplectic group over a field of characteristic \(2\) and the defective orthogonal groups.
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 1337569
zbMATH Keywords: hyperbolic unitary groups
zbMATH Keywords: form rings
zbMATH Keywords: overdiagonal subgroups
zbMATH Keywords: lattices of subgroups
MaRDI profile type: Publication
cites work: Q4138920
cites work: Q3887658
cites work: Q3208885
cites work: Q3791349
cites work: Q3921406
cites work: Q4396666
cites work: On the net subgroups conjugacy in a hyperbolic unitary group over a field.
cites work: Structure of Hyperbolic Unitary Groups I: Elementary Subgroups
cites work: Subgroups of the special linear group containing the diagonal subgroup
full work available at URL: https://doi.org/10.1007/bf02169965
OpenAlex ID: W2053562647
description: scientific article; zbMATH DE number 1337569