Chapter XII: Tables

Abstract

The tables given in this chapter contain the classification and the most basic information about simple Jordan algebras, -triple systems and -pairs and about their associated symmetric spaces. We use the classification principle explained in Section IV.2. Most of the material given here has already been presented in form of examples (Sections I.6, IV.1, VIII.4, IX.2, X.1, X.2, XI.5); therefore we will not repeat calculations. The aim of this chapter is to provide reference material in a concise form; the results themselves axe essentially all known from work of K.-H. Helwig, B.O. Makarevič, E. Neher and others (see the notes), but some of them axe not easily accessible for non-specialists. We have not included the exceptional spaces and refer to the work of E. Neher ([Ne81], [Ne85]) for this.