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- Title
Quaternary binary trilinear forms of norm unity.
- Authors
Bernhardsson, Bo; Cobos, Fernando; Kühn, Thomas; Mondoc, Daniel; Peetre, Jaak
- 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 H and the commutative one of R and C.
- Subjects
TRILINEAR forms; SCALAR field theory; REAL numbers; QUATERNIONS; WOLFRAM language (Computer program language)
- Publication
Proceedings of the Estonian Academy of Sciences, Physics, Mathematics, 2006, Vol 55, Issue 3, p150
- ISSN
1406-0086
- Publication type
Article
- DOI
10.3176/phys.math.2006.3.04