STUDY ON HOPF-GALOIS THEORY

1. Y.Doi和M.Takeuchi，关于llopf代数的上循环变形，1996（日文）：本文是第一作者在1993年通过研究辫子双代数和二次双代数引入的关于Hopf代数的上循环变形的概述。Y.土井，霍普夫代数和环理论-Frobenius扩张的一些主题-，1997（日语）：我在这里给出了有限维llopf代数的Frobenius性的自然证明。作为应用，给出了Schneider关于β-Frobenius扩张定理的一个快速证明. Y.Doi，A note on Frobenius extensions in Hopf algebras，1997：本文研究了Hopf子代数上的Hopf代数的Frobenius性质的条件。其中给出了Hopf代数扩张成为Schneider意义下的右积分型的一个很好的条件. Y.Doi，An introduction to separable lllopf algebras，1997：这篇文章是一个关于可分Hopf代数的快速介绍。它包含了Larson-Radford迹公式的一种新的方法。Y.Doi，Yetter-Drinfeld范畴中的Hopf模，1998：本文研究了Hopf代数上的Yetter-Drinfeld模范畴中的llopf模和Hopf代数对象的基本性质。

1. Y.Doi and M.Takeuchi, On cocycle deformations of llopf algebras, 1996 (in Japanese) : This paper is an outline about cocycle deformations of Hopf algebras, which is introduced in 1993 by the first author through his study of braided and quadratic bialgebras.2. Y.Doi, Hopf algebras and ring theory -some topics on Frobenius extensions-, 1997 (in Japanese) : I give here a natural proof for Frobeniusness of finite dimensional llopf algebras. As an application I give a quick proof of Schneider' s theorem about beta-Frobenius extensions.3. Y.Doi, A note on Frobenius extensions in Hopf algebras, 1997 : This paper studies conditions on Frobenius property of Hopf algebras over Hopf sub-algebras. ln it I give a nice condition for extensions of Hopf algebras becoming of right integral type in the sense of Schneider.4. Y.Doi, An introduction to separable llopf algebras, 1997 : This paper is a quick introduction about separable Hopf algebras for ring theorists. It contains a new approach of the trace formulae of Larson-Radford.5. Y.Doi, Hopf modules in Yetter-Drinfeld categories, 1998 : This paper studies basic properties on llopf modules and Hopf algebra objects in the categories of Yetter-Drinfeld modules over a Hopf algebra.