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Homological integral of Hopf algebras


Authors: D.-M. Lu, Q.-S. Wu and J. J. Zhang
Journal: Trans. Amer. Math. Soc. 359 (2007), 4945-4975
MSC (2000): Primary 16A62, 16W30; Secondary 16E70, 20J50
DOI: https://doi.org/10.1090/S0002-9947-07-04159-1
Published electronically: May 16, 2007
MathSciNet review: 2320655
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Abstract: The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschke's theorem for infinite dimensional Hopf algebras. The generalization of Maschke's theorem and homological integrals are the keys to studying noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.


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Additional Information

D.-M. Lu
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
Email: dmlu@zju.edu.cn

Q.-S. Wu
Affiliation: Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Email: qswu@fudan.edu.cn

J. J. Zhang
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Email: zhang@math.washington.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04159-1
Keywords: Hopf algebra, homological integral, Gorenstein property, regularity, Gelfand-Kirillov dimension, integral order, integral quotient, PI degree
Received by editor(s): May 16, 2005
Received by editor(s) in revised form: July 11, 2005
Published electronically: May 16, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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