Pointed Hopf algebras of finite corepresentation type and their classifications
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- by Gongxiang Liu and Fang Li PDF
- Proc. Amer. Math. Soc. 135 (2007), 649-657 Request permission
Abstract:
Let $k$ be an algebraically closed field. The main goal of this paper is to classify the finite-dimensional pointed Hopf algebras over $k$ of finite corepresentation type. To do so, we give a necessary and sufficient condition for a basic Hopf algebra over $k$ to be of finite representation type firstly. Explicitly, we prove that a basic Hopf algebra over $k$ is of finite representation type if and only if it is Nakayama. By this conclusion, we classify all finite-dimensional pointed Hopf algebras over $k$ of finite corepresentation type.References
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Additional Information
- Gongxiang Liu
- Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
- MR Author ID: 766485
- Email: gxliu@amss.ac.cn
- Fang Li
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310028, People’s Republic of China
- Email: fangli@zju.edu.cn
- Received by editor(s): September 11, 2004
- Received by editor(s) in revised form: September 10, 2005, and September 23, 2005
- Published electronically: August 31, 2006
- Additional Notes: This project was supported by the Program for New Century Excellent Talents in University (No.04-0522), the Natural Science Foundation of Zhejiang Province of China (No.102028) and partially by the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No.704004).
- Communicated by: Martin Lorenz
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 649-657
- MSC (2000): Primary 16G20, 16G30, 16W30
- DOI: https://doi.org/10.1090/S0002-9939-06-08504-2
- MathSciNet review: 2262859