The construction of homogeneous convex cones

An open convex cone D in E is called homogeneous if the subgroup of linear transformations of E leaving D invariant, called the group of automorphisms of D, acts transitively on D. In this note we indicate briefly an inductive procedure by means of which all homogeneous convex cones may be constructed. Details of the construction will be given elsewhere. The dual of the convex cone D is defined to be the set