| Hopf-Galois coextensions and braided Lie coalgebras |
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| 作者姓名： | WANG Shuanhong CHEN Huixiang |
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| 作者单位： | Department of Mathematics, Henan Normal University, Xinxiang 453002, China,Department of Mathematics, Yangzhou University, Yangzhou 225002, China |
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| 基金项目： | Supported partially by the National Natural Science Foundation of China (Grant Nos. 19601015, 19971073) And Natural Science Foundation of Henan Province |
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| 摘 要： | Let k be a commutative ring and H a k-bialgebra. Assume that there exists an H-cogalois right H-module coalgebra C such that C is faithfully k-flat. We show that H is necessarily a Hopf algebra. Then the Lie coalgebras in Yetter-Drinfeld categories H HYD (braided Lie coalgebras) are studied. In particular, a necessary and sufficient condition for the natural map Γ C(U CM)→M to be surjective is given.
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| 关 键 词： | Hopf algebras Hopf-Galois coextensions braided Lie coalgebras Yetter-Drinfeld categories |
Hopf-Galois coextensions and braided Lie coalgebras |
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| WANG Shuanhong,CHEN Huixiang.Hopf-Galois coextensions and braided Lie coalgebras[J].Progress in Natural Science,2002,12(4):264-270. |
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| Authors: | WANG Shuanhong CHEN Huixiang |
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| Institution: | 1. Department of Mathematics, Henan Normal University, Xinxiang 453002, China
2. Department of Mathematics, Yangzhou University, Yangzhou 225002, China |
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| Abstract: | Let k be a commutative ring and H a k-bialgebra. Assume that there exists an H-cogalois right H-module coalgebra C such that C is faithfully k-flat. We show that H is necessarily a Hopf algebra. Then the Lie coalgebras in Yetter-Drinfeld categories H HYD (braided Lie coalgebras) are studied. In particular, a necessary and sufficient condition for the natural map Γ C(U CM)→M to be surjective is given. |
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| Keywords: | Hopf algebras Hopf-Galois coextensions braided Lie coalgebras Yetter-Drinfeld categories |
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