Die struktur endlicher schwach abgeschlossener Jordanalgebren Teil II. Diskrete Jordanalgebren

Abstract

In the preceding note [6] we reduced the study of continuous finite weakly closed Jordan algebras to real associative W*-algebras of type II1. Here we treat the remaining case of discrete finite weakly closed Jordan algebras and describe them completely by finite dimensional simple formally real Jordan algebras and by simple formally real Jordan algebras of quadratic forms of real Hilbert spaces. Jacobsons theory of Jordan algebras with minimum condition combined with W*-algebra techniques constitutes an essential tool in the proof.