On semisimple Hopf algebras of dimension

Authors:
Shlomo Gelaki and Sara Westreich

Journal:
Proc. Amer. Math. Soc. **128** (2000), 39-47

MSC (1991):
Primary 16W30

DOI:
https://doi.org/10.1090/S0002-9939-99-04961-8

Published electronically:
June 24, 1999

Erratum:
Proc. Amer. Math. Soc. 128 (2000), 2829-2831.

MathSciNet review:
1618670

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of the classification of semisimple Hopf algebras of dimension where are two prime numbers. First we prove that the order of the group of grouplike elements of is not , and that if it is , then . We use it to prove that if and its dual Hopf algebra are of Frobenius type, then is either a group algebra or a dual of a group algebra. Finally, we give a complete classification in dimension , and a partial classification in dimensions and .

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Additional Information

**Shlomo Gelaki**

Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

Address at time of publication:
Department of Mathematics, University of Southern California, Los Angeles, California 90089

Email:
gelaki@math.usc.edu

**Sara Westreich**

Affiliation:
Interdisciplinary Department of the Social Science, Bar-Ilan University, Ramat-Gan, Israel

Email:
swestric@mail.biu.ac.il

DOI:
https://doi.org/10.1090/S0002-9939-99-04961-8

Received by editor(s):
August 1, 1997

Received by editor(s) in revised form:
March 17, 1998

Published electronically:
June 24, 1999

Additional Notes:
The second author’s research was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities

Communicated by:
Lance W. Small

Article copyright:
© Copyright 1999
American Mathematical Society