A note on the bijectivity of the antipode of a Hopf algebra and its applications
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Abstract:
Certain sufficient homological and ring-theoretical conditions are given for a Hopf algebra to have a bijective antipode with applications to noetherian Hopf algebras regarding their homological behaviors.References
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Additional Information
- Jiafeng Lü
- Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, People’s Republic of China
- Email: jiafenglv@zjnu.edu.cn
- Sei-Qwon Oh
- Affiliation: Department of Mathematics, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, South Korea
- MR Author ID: 340162
- Email: sqoh@cnu.ac.kr
- Xingting Wang
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- Address at time of publication: Department of Mathematics, Howard University, Washington DC, 20059
- MR Author ID: 1029882
- Email: wangxingting84@gmail.com
- Xiaolan Yu
- Affiliation: Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, People’s Republic of China
- MR Author ID: 921105
- Email: xlyu@hznu.edu.cn
- Received by editor(s): September 22, 2017
- Received by editor(s) in revised form: February 22, 2018
- Published electronically: August 7, 2018
- Additional Notes: The first author was supported by the National Natural Science Foundation of China, No. 11571316 and No. 11001245, and the Natural Science Foundation of Zhejiang Province, No. LY16A010003.
The second author was supported by the National Research Foundation of Korea, NRF-2017R1A2B4008388.
The third author was supported by an AMS–Simons travel grant.
The fourth author was supported by the National Natural Science Foundation of China, No. 11301126, No. 11571316, and No. 11671351. - Communicated by: Kailash C. Misra
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4619-4631
- MSC (2010): Primary 16E65, 16W30, 16W35
- DOI: https://doi.org/10.1090/proc/14140
- MathSciNet review: 3856132