We show that an order antimorphism on a finite-dimensional cone having no one-dimensional factors is homogeneous of degree \(-\,1\). A consequence is that the only finite-dimensional cones admitting an order antimorphism are the symmetric cones.

中文翻译：

---

有限维锥的阶反态

我们表明，在没有一维因素的有限维圆锥上的阶反同构是度\（-\，1 \）的齐次。结果是，允许阶次同态性的唯一有限维圆锥是对称圆锥。