On connection algebras of homogeneous convex cones (Q790922)

The main result of this paper is: If the connection algebra of a homogeneous cone V is power-associative, then V is self-dual. As pointed out in the paper this result follows immediately from a result of the reviewer. The approach used here is more direct and uses Vinberg's T- algebras rather than the reviewer's algebraic structures. The main result is followed by a nice collection of properties of a homogeneous cone V which are equivalent to V being self-dual.