| Monomial Hopf algebras over fields of positive characteristic |
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| 作者姓名： | LIU Gongxiang & YE Yu Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China |
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| 作者单位： | LIU Gongxiang & YE Yu Institute of Mathematics，Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China; Department of Mathematics，University of Science and Technology of China，Hefei 230026，China |
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| 基金项目： | the Program for New Century Excellent Talents in University，the second author was supported by the National Natural Science Foundation of China，the Doctoral Foundation of the Chinese Education Ministry |
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| 摘 要： | In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n) are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.
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| 收稿时间： | 8 October 2004 |
| 修稿时间： | 3 November 2005 |
Monomial Hopf algebras over fields of positive characteristic |
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| LIU Gongxiang & YE Yu Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing ,China,.Monomial Hopf algebras over fields of positive characteristic[J].Science in China(Mathematics),2006,49(3):320-329. |
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| Authors: | LIU Gongxiang YE Yu |
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| Institution: | 1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100080, China
2. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
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| Abstract: | In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n) are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras. |
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| Keywords: | monomial coalgebra Gaussian binomial coefficient monomial Hopf algebra |
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