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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

MR Author ID:
314509

Email:
zhang@math.washington.edu

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.