A characterization of the semi-isometries of a Minkowski plane over a field K
This is a deep and beautiful result on the characterization of Lorentz transformations in the plane over a field. More precisely: Suppose that K is a field of characteristics \(\neq 2\), 3, 5 or that \(K=GF(5^ m), m>1\). Suppose moreover that \(\sigma:K^ 2\to K^ 2\) is a mapping preserving the Lorentz-Minkowski distance 1. Then \(\sigma\) must be a Lorentz transformation of \(K^ 2\) up to a translation and up to a monomorphism of the field K. In the proof of this theorem there was also used a computer in order to construct very special configurations needed. Beyond it the proof works with tools of Minkowski's geometry and algebra.
scientific article; zbMATH DE number 3872157
scientific article