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A note on the bijectivity of the antipode of a Hopf algebra and its applications


Authors: Jiafeng Lü, Sei-Qwon Oh, Xingting Wang and Xiaolan Yu
Journal: Proc. Amer. Math. Soc. 146 (2018), 4619-4631
MSC (2010): Primary 16E65, 16W30, 16W35
DOI: https://doi.org/10.1090/proc/14140
Published electronically: August 7, 2018
MathSciNet review: 3856132
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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.


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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
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
Email: wangxingting84@gmail.com

Xiaolan Yu
Affiliation: Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, People’s Republic of China
Email: xlyu@hznu.edu.cn

DOI: https://doi.org/10.1090/proc/14140
Keywords: Antipode, Hopf algebra, Calabi--Yau algebra, AS-Gorenstein, AS-regular
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
Article copyright: © Copyright 2018 American Mathematical Society