Algebraic description of homogeneous cones

Abstract

This paper finishes the author’s investigations on homogeneous cones. As a result a classification of homogeneous cones is derived. The most important tool to get insight into the structure of homogeneous cones are J-morphisms. Therefore, in this paper we mainly deal with morphisms of homogeneous cones. The main result gives an algebraic description of J-morphisms. It includes a description of “Linear imbeddings of self-dual homogeneous cones” and the above mentioned classification of homogeneous cones. In a subsequent paper it will be used to describe homogeneous Siegel domains.