Quaternary Binary Trilinear forms of Norm Unity

Ühiknormiga kvaternaarsetest binaarsetest kolmlineaarsetest vormidest

Bo Bernhardsson ； Fernando Cobosb ； Thomas Kühn ； Daniel Mondoc ； Jaak Peetree

《Proceedings of the Estonian Academy of Sciences. Physics, Mathematics》 55卷3期 (2006/09) Pp. 150-158

並列摘要

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.

並列關鍵字

trilinear form ； quaternion ； discriminant ； principal minor