TY - JOUR

T1 - On semisimple Hopf algebras of dimension pq

AU - Gelaki, Shlomo

AU - Westreich, Sara

PY - 2000

Y1 - 2000

N2 - We consider the problem of the classification of semisimple Hopf algebras A of dimension pq where p < q are two prime numbers. First we prove that the order of the group of grouplike elements of A is not q, and that if it is p, then q = 1 (mod p). We use it to prove that if A and its dual Hopf algebra A* are of Frobenius type, then A is either a group algebra or a dual of a group algebra. Finally, we give a complete classification in dimension 3p, and a partial classification in dimensions 5p and 7p.

AB - We consider the problem of the classification of semisimple Hopf algebras A of dimension pq where p < q are two prime numbers. First we prove that the order of the group of grouplike elements of A is not q, and that if it is p, then q = 1 (mod p). We use it to prove that if A and its dual Hopf algebra A* are of Frobenius type, then A is either a group algebra or a dual of a group algebra. Finally, we give a complete classification in dimension 3p, and a partial classification in dimensions 5p and 7p.

UR - http://www.scopus.com/inward/record.url?scp=22844457063&partnerID=8YFLogxK

U2 - 10.1090/s0002-9939-99-04961-8

DO - 10.1090/s0002-9939-99-04961-8

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SN - 0002-9939

VL - 128

SP - 39

EP - 47

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -