Generation of integral orthogonal groups over dyadic local fields
type: Item
instance of: scholarly article
title: Generation of integral orthogonal groups over dyadic local fields
zbMATH Open document ID: 0829.11021
author: Fei Xu
published in: Pacific Journal of Mathematics
publication date: 1996-01-22T00:00:00Z
review text: Consider a dyadic field \(F\). Let \(V\) be a regular quadratic space over \(F\) and let \(L\) be a lattice on \(V\). The main theorem of the paper under review states that the orthogonal group \(O(L)\) of \(L\) is generated by symmetries and Eichler transformations unless the image of \(O(L)\) under the spinor norm coincides with the multiplicative group of \(F\). The same statement holds if \(L\) is modular or 2 is unramified. The latter result is due to O'Meara and Pollak. The author introduces the notion of `minimal norm Jordan splittings' and combines some of his earlier results with the techniques of O'Meara and Pollak for the proof of his main theorem. One possible application is to study the spinor genus theory over number fields. This will be done in a joint paper of the author, Hsia and Shao.
Mathematics Subject Classification ID: 11E08
Mathematics Subject Classification ID: 11E57
zbMATH DE Number: 769667
zbMATH Keywords: modular lattice
zbMATH Keywords: minimal norm Jordan splittings
zbMATH Keywords: dyadic field
zbMATH Keywords: lattice
zbMATH Keywords: orthogonal group
reviewed by: Martin Epkenhans
MaRDI profile type: Publication
full work available at URL: pjm.1995.167.385
OpenAlex ID: W2035673662
DOI: 10.2140/PJM.1995.167.385
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description: scientific article; zbMATH DE number 769667