RT Journal Article
T1 Quaternary binary trilinear forms of norm unity
A1 Bernhardsson, Bo
A1 Cobos Díaz, Fernando
A1 Kühn, Tomas
A1 Mondoc, Daniel
A1 Peetre, Jaak
AB 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.
PB Estonian Academy of Sciences
SN 1736-6046
YR 2006
FD 2006
LK https://hdl.handle.net/20.500.14352/50766
UL https://hdl.handle.net/20.500.14352/50766
LA eng
NO Ministerio de Ciencia, Innovación y Universidades (España)
DS Docta Complutense
RD 17 abr 2025