Order antimorphisms of finite-dimensional cones
The author expands the study of the automorphisms of open cones in finite-dimensional convex geometry, which goes back to \textit{A. D. Aleksandrov} and \textit{V. V. Ovchinnikova} [``Notes on the foundations of relativity theory'' (Russian), Vestn. Leningr. Univ., Mat. Mekh. Astron. 11, 95--110 (1953), per bibl.], by addressing the properties of antimorphisms of the cones. The main result states that, if \(\Phi: C\to C \) is an order antimorphism between two proper open convex cones in a finite-dimensional vector and \(C\) has no one-dimensional factors, then \(\Phi\) is antihomogeneous.
scientific article; zbMATH DE number 7229493
scientific article