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Homological integral of Hopf algebras

Author(s): D.-M. Lu; Q.-S. Wu; J. J. Zhang
Journal: Trans. Amer. Math. Soc. 359 (2007), 4945-4975.
MSC (2000): Primary 16A62, 16W30; Secondary 16E70, 20J50
Posted: May 16, 2007
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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: 10.1090/S0002-9947-07-04159-1
PII: S 0002-9947(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
Posted: May 16, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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