On Noetherian affine prime regular Hopf algebras of Gelfand-Kirillov dimension 1

Author:
Gongxiang Liu

Journal:
Proc. Amer. Math. Soc. **137** (2009), 777-785

MSC (2000):
Primary 16W30

DOI:
https://doi.org/10.1090/S0002-9939-08-09034-5

Published electronically:
October 29, 2008

MathSciNet review:
2457414

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an algebraically closed field. In 2007, D.-M. Lu, Q.-S. Wu, and J. J. Zhang asked the following question: Besides the group algebras and infinite dimensional prime Taft algebras, are there other noetherian affine prime regular Hopf algebras of GK-dimension 1? In this paper, we give a new one. Another problem posed by Lu, Wu, and Zhang can also be resolved by this example. Assuming is a noetherian affine prime regular Hopf algebra of GK-dimension 1, we show that gr , as a Hopf algebra, is isomorphic to an infinite dimensional prime Taft algebra. This gives a characterization of infinite dimensional prime Taft algebras.

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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

Address at time of publication:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Email:
gxliu@nju.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-08-09034-5

Keywords:
Homological integral,
Gelfand-Kirillov dimension

Received by editor(s):
September 25, 2006

Received by editor(s) in revised form:
March 25, 2007

Published electronically:
October 29, 2008

Additional Notes:
Project supported by the Natural Science Foundation of China (No. 10801069).

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.