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Hopf algebras of dimension $2p$

Author(s): Siu-Hung Ng
Journal: Proc. Amer. Math. Soc. 133 (2005), 2237-2242.
MSC (2000): Primary 16W30
Posted: February 15, 2005
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Abstract: Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If $H$ is not semisimple and $\dim(H)=2n$ for some odd integer $n$, then $H$ or $H^*$ is not unimodular. Using this result, we prove that if $\dim(H)=2p$ for some odd prime $p$, then $H$ is semisimple. This completes the classification of Hopf algebras of dimension $2p$.

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Additional Information:

Siu-Hung Ng
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: rng@math.iastate.edu

DOI: 10.1090/S0002-9939-05-07804-4
PII: S 0002-9939(05)07804-4
Keywords: Finite-dimensional Hopf algebras
Received by editor(s): November 24, 2003
Received by editor(s) in revised form: April 7, 2004
Posted: February 15, 2005
Communicated by: Martin Lorenz
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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