antipode

In the paper we give the notion of the antipode and present its special features.

在本文中，我们给出对极的定义以及它的特殊性质。

The South Pole is the antipode of the North Pole.

南极是北极的对跖地.

On the antipode and group-like elements of a braided Hopf algebra

辫子Hopf代数上的对极与类群元

Let H be an arbitrary Hopf algebra over a field k with bijective antipode s.

设H是定义在域k上的一个Hopf代数，反极元s为双射。

But a hypothetically perfect antipode flight would be Tangier Ibn Battouta Airport, Morocco to Whangarei Aerodrome, New Zealand, a flight of approximately 20000km.

不过理想中的航线是从摩洛哥的丹吉尔机场飞至新西兰的旺阿雷机场，全程约20000公里。

" We just sit and listen to the fullness of the quiet, as an antipode to focused busyness"( Kathryn A.Knox)

“我们坐下来享受一下完全安静的环境，这是和高度繁忙恰恰相反的”（凯瑟琳A。诺克斯）

The antipode of love is hatred.

爱的反面是恨。

Virtue is the antipode of selfishness.

道德与自私相反.

For the ×-R-Hopf algebras the generalization of the fundamental structure theorem of Hopf modules is given by introducing the definition of antipode.

在引入了对极的概念之后并将基本结构定理推广到×R Hopf代数上的Hopf模上。