Order antimorphisms of finite-dimensional cones
type: Item
instance of: scholarly article
title: Order antimorphisms of finite-dimensional cones
zbMATH Open document ID: 1447.46003
author: Cormac Walsh
published in: Selecta Mathematica. New Series
publication date: 2020-08-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 7229493
zbMATH Keywords: finite-dimensional real vector space
zbMATH Keywords: positive cone
zbMATH Keywords: antimorphism
zbMATH Keywords: symmetric cone
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
full work available at URL: s00029-020-00583-5
OpenAlex ID: W2894836407
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DOI: 10.1007/S00029-020-00583-5
description: scientific article; zbMATH DE number 7229493