北京大学学报(自然科学版)

R-余环与×R-Hopf 代数上的范畴

殷艳敏, 刘张炬   

  1. 北京大学数学科学学院,北京,100871
  • 收稿日期:2002-11-18 出版日期:2003-09-20 发布日期:2003-09-20

The R-Coring and the ×R-Hopf Algebra

YIN Yanmin, LIU Zhangju   

  1. School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:2002-11-18 Online:2003-09-20 Published:2003-09-20

摘要: ×R-双代数L的左模范畴与左L*-模范畴是等价的。左(L,A)-Hopf模范畴同构于左A#L*- 模范畴。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。

关键词: smash积, 对极, 基本结构定理, ×R-Hopf代数

Abstract: It is proved that the category of the left comodules over the ×R-bialgebra L is equivalent to the category of the left L*-modules, and the monoidal functor from LAM to A#L*-module is equivalent.For the ×R-Hopf algebras the generalization of the fundamental structure theorem of Hopf modules is given by introducing the definition of antipode.

Key words: ×R-Hopf algebra, smash product, antipode, fundamental structure theorem

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