A note on the linkage of Hurwitz algebras
type: Item
instance of: scholarly article
title: A note on the linkage of Hurwitz algebras
zbMATH Open document ID: 1103.11014
author: Alberto Elduque
author: Oliver Villa
published in: Manuscripta Mathematica
publication date: 2005-06-13T00:00:00Z
review text: Let \(F\) be a field of characteristic~\(2\). The Hurwitz algebras considered in this paper are the quaternion and the octonion \(F\)-algebras. (Octonion algebras are also called Cayley algebras.) Hurwitz \(F\)-algebras are called left linked when they contain isomorphic separable quadratic extensions of \(F\), and right linked when they contain isomorphic inseparable quadratic extensions of \(F\). This terminology was inspired by \textit{T.-Y. Lam}, who investigated the linkage of quaternion \(F\)-algebras in [On the linkage of quaternion algebras, Bull. Belg. Math. Soc.-Simon Stevin 9, No.~3, 415--418 (2002; Zbl 1044.16012)]. In this paper, the authors extend Lam's results to arbitrary Hurwitz algebras. They show that two Hurwitz \(F\)-algebras are left linked if they are right linked, and give an example of two octonion \(F\)-algebras that are left linked but not right linked.
Mathematics Subject Classification ID: 11E88
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12F15
Mathematics Subject Classification ID: 16K20
zbMATH DE Number: 2175526
zbMATH Keywords: quaternion algebras
zbMATH Keywords: octonion algebras
zbMATH Keywords: Cayley algebras
zbMATH Keywords: quadratic forms
reviewed by: Jean-Pierre Tignol
MaRDI profile type: Publication
full work available at URL: s00229-004-0512-7
OpenAlex ID: W2091095251
cites work: Quadratic forms over semilocal rings
cites work: Q4298904
cites work: Q4210545
cites work: On the linkage of quaternion algebras.
cites work: Q4298903
DOI: 10.1007/S00229-004-0512-7
description: scientific article; zbMATH DE number 2175526