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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pointed Hopf algebras of finite corepresentation type and their classifications


Authors: Gongxiang Liu and Fang Li
Journal: Proc. Amer. Math. Soc. 135 (2007), 649-657
MSC (2000): Primary 16G20, 16G30, 16W30
Published electronically: August 31, 2006
MathSciNet review: 2262859
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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.


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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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08504-2
PII: S 0002-9939(06)08504-2
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
Article copyright: © Copyright 2006 American Mathematical Society