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HOPF ALGEBRAS OF DIMENSION 14

Published online by Cambridge University Press:  28 January 2004

M. BEATTIE  and
S. DĂSCĂLESCU
M. BEATTIE
Affiliation:
Mount Allison University, Department of Mathematics and Computer Science, Sackville, NB, Canada E4L 1E6
S. DĂSCĂLESCU
Affiliation:
Department of Mathematics, Faculty of Science, Kuwait University, PO Box 5969, Safat 13060, Kuwait
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Abstract

Let $H$ be a finite dimensional non-semisimple Hopf algebra over an algebraically closed field $k$ of characteristic 0. If $H$ has no nontrivial skew-primitive elements, some bounds are found for the dimension of $H_1$, the second term in the coradical filtration of $H$. Using these results, it is shown that every Hopf algebra of dimension 14 is semisimple and thus isomorphic to a group algebra or the dual of a group algebra. Also a Hopf algebra of dimension $pq$ where $p$ and $q$ are odd primes with $p < q \leq 1 + 3p$ and $q \leq 13$ is semisimple and thus a group algebra or the dual of a group algebra. Some partial results in the classification problem for dimension 16 are also given.

Keywords

16W30
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 65 - 78
Copyright
The London Mathematical Society 2004

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