Geometric description of the unit ball of a neutral strongly facially symmetric space

Abstract

 This paper is devoted to the study of the geometric structure of neutral strongly facially symmetric (SFS) spaces, which provide a natural framework for modeling aspects of quantum mechanics in geometric terms. We investigate the representation of symmetric faces associated with complete and maximal geometric tripotents and establish their connections with split faces. Based on these results, we obtain a geometric description of the unit ball in neutral SFS-spaces. Furthermore, we give a characterization of real neutral SFS-spaces, highlighting their structural properties and the role of geometric tripotents in determining the organization of the unit ball.