Pfaffians and determinant of E. H. Moore
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.
central simple algebras with involutions
scientific article; zbMATH DE number 1421343