| 一类半单Hopf代数的结构 |
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| 引用本文： | 董井成.一类半单Hopf代数的结构[J].数学学报,2011(2):293-300. |
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| 作者姓名： | 董井成 |
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| 作者单位： | 扬州大学数学科学学院;南京农业大学工学院; |
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| 基金项目： | 国家自然科学基金资助项目(10771183); 教育部博士点基金资助项目(200811170001) |
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| 摘 要： | 设k是特征为零的代数闭域,H是k上的pq~2维Frobenius型半单Hopf代数,其中p,q为不同的素数.本文证明了,如果p>q且H~*也是Frobenius型Hopf代数,则H是q~2维群代数A与A上p维Yetter-Drinfeld Hopf代数R的双积,即H≌R#A.作为例子,本文还证明了任意63维或68维的半单Hopf代数均为Frobenius型Hopf代数.
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| 关 键 词： | 半单Hopf代数 Kaplansky第六猜想 双积 |
Structure of a Class of Semisimple Hopf Algebras |
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| Jing Cheng DONG School of Mathematics,Yangzhou University,Yangzhou ,P.R.China College of Engineering,Nanjing Agricultural University,Nanjing ,P.R.China.Structure of a Class of Semisimple Hopf Algebras[J].Acta Mathematica Sinica,2011(2):293-300. |
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| Authors: | Jing Cheng DONG School of Mathematics Yangzhou University Yangzhou PRChina College of Engineering Nanjing Agricultural University Nanjing PRChina |
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| Institution: | Jing Cheng DONG School of Mathematics,Yangzhou University,Yangzhou 225002,P.R.China College of Engineering,Nanjing Agricultural University,Nanjing 210031,P.R.China |
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| Abstract: | Let k be an algebraically closed field of characteristic zero,H a semisimple Hopf algebra of dimension pq~2 of Frobenius type,where p,q are distinct prime numbers. This paper proves that if p>q and H~* is also of Frobenius type then H is a biproduct of a group algebra A of dimension q~2 and a Yetter-Drinfeld Hopf algebra R over A of dimension p.That is H≌R#A.As an example,this paper then proves that every semisimple Hopf algebra of dimension 63 or 68 is of Frobenius type. |
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| Keywords: | semisimple Hopf algebra Kaplansky's sixth conjecture biproduct |
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