1998 Fiscal Year Final Research Report Summary
STUDY ON HOPF-GALOIS THEORY
| Project/Area Number |
08640020
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Fukui University |
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Principal Investigator |
DOI Yukio FUKUI UNIVERSITY,FACULTY OF EDUCATION,PROFESSOR, 教育学部, 教授 (50015765)
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| Project Period (FY) |
1996 – 1998
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| Keywords | Hopf algebra / cocycle deformation / Frobenius extension / trace formula / Yetter-Drinfeld module |
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| Research Abstract |
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.
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