Pfaffians and determinant of E. H. Moore
type: Item
instance of: scholarly article
title: Pfaffians and determinant of E. H. Moore
zbMATH Open document ID: 0958.16017
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2001-04-02T00:00:00Z
review text: For a Hermitian matrix over the quaternions (over any field of characteristic \(\neq 2\)) a determinant can be defined (E. H. Moore determinant) which is a polynomial in the entries and represents the Dieudonné determinant [\textit{P. Van Praag}, J. Algebra 136, No. 2, 265-274 (1991; Zbl 0724.15013)]. \textit{M.-A. Knus}, \textit{R. Parimala} and \textit{R. Sridharan} [Bull. Soc. Math. Belg., Sér. A 43, No. 1/2, 89-98 (1991; Zbl 0757.12002)] defined a notion of Pfaffian for every central simple algebra with an involution, which in the symplectic case coincides with the reduced norm of the Jordan algebra of symmetric elements, called reduced Pfaffian norm [\textit{M.-A. Knus}, \textit{A. Merkurjev}, \textit{M. Rost} and \textit{J.-P. Tignol}, The book of involutions, Coll. Publ. Am. Math. Soc. 44 (1998; Zbl 0955.16001)]. The author proves here that for the quaternions over a field of characteristic \(\neq 2\) these two notions coincide.
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 12E15
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 1421343
zbMATH Keywords: central simple algebras with involutions
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: quaternions
zbMATH Keywords: Moore determinants
zbMATH Keywords: Dieudonné determinants
zbMATH Keywords: reduced norms
zbMATH Keywords: Jordan algebras
author: Jean-Pierre Tignol
reviewed by: Paul M. Cohn
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1421343