Characters of central piques. (Q1880680)

The author presents an explicit computation of the characters of a central pique using Wigner's little groups method. Character theory for finite quasigroups was introduced by the author (see his papers about). The character theory of Abelian groups exhibits special features, generally arising from duality theory for Abelian groups that finds its fullest and most satisfactory formulation in the topological context of Pontryagin duality for locally compact Abelian groups. This paper represents a first step toward the investigation of these special features according to the author. To simplify the presentation, the paper focusses on central piques. Thus one of the main goals is to provide an explicit determination of the character table of a finite central pique.