Quaternary binary trilinear forms of norm unity

Bernhardsson, Bo; Cobos Díaz, Fernando; Kühn, Tomas; Mondoc, Daniel; Peetre, Jaak

Quaternary binary trilinear forms of norm unity

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Cobos-Quaternary.pdf (156.17 KB)

Official URL

http://www.kirj.ee/public/va_fm/phys-2006-3-4.pdf

Publication date

2006

Authors

Bernhardsson, Bo

Cobos Díaz, Fernando

Kühn, Tomas

Mondoc, Daniel

Peetre, Jaak

Publisher

Estonian Academy of Sciences

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URI

https://hdl.handle.net/20.500.14352/50766

Abstract

So far trilinear forms have mostly been considered in low dimensions, in particular the dimension two (binary) case, and when the ring of scalars K is either the real numbers R or the complex ones C. The main aim in both situations has been to decide when a normalized form has norm unity. Here we consider the case of quaternions, K = H. This note is rather preliminary, and somewhat experimental, where the computer program Mathematica plays a certain role. A preliminary result obtained is that the form has norm unity if and only if the discriminant of a certain 5-dimensional quadratic form has all its principal minors nonnegative. We found also a rather unexpected similarity between the noncommutative case of Hnand the commutative one of R and C.