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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
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 -