The Structure of Semisimple Associative and Jordan Algebras

Abstract

Following the general algebra background work of the last chapter, we are now in a position to specialize our algebras to the kind we will encounter in the structure theory of variance components. Thus we present the complete classification of finite dimensional semisimple associative algebras and also that of finite dimensional semisimple Jordan algebras which are generated by sets of real symmetric matrices. The classification of all the simple Jordan algebras of this form is evidently a new result.