%0 Journal Article
%A Bernhardsson, Bo
%A Cobos Díaz, Fernando
%A Kühn, Tomas
%A Mondoc, Daniel
%A Peetre, Jaak
%T Quaternary binary trilinear forms of norm unity
%D 2006
%@ 1736-6046
%U https://hdl.handle.net/20.500.14352/50766
%X 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.
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