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Journal of the London Mathematical Society 2004 69(1):65-78; doi:10.1112/S0024610703004927
© 2004 by London Mathematical Society
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© The London Mathematical Society

Hopf Algebras of Dimension 14

M. Beattie and S. Dascalescu

Mount Allison University, Department of Mathematics and Computer Science Sackville, NB, Canada E4L 1E6
Department of Mathematics, Faculty of Science, Kuwait University PO Box 5969, Safat 13060, Kuwait

Received 23 May 2002. Revision received 20 March 2003.

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 H1, 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 ≤ 1 + 3p and q ≤ 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.


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