On semisimple Hopf algebras of dimension ![]() |
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| Authors: | Shlomo Gelaki Sara Westreich |
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| Institution: | Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 ; Interdisciplinary Department of the Social Science, Bar-Ilan University, Ramat-Gan, Israel |
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| 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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