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Semisimple Hopf Algebras of DimensionpqAre Trivial

✍ Scribed by Pavel Etingof; Shlomo Gelaki

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
65 KB
Volume
210
Category
Article
ISSN
0021-8693

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✦ Synopsis

This paper makes a contribution to the problem of classifying finitedimensional semisimple Hopf algebras H over an algebraically closed field k of characteristic 0. Specifically, we show that if H has dimension pq for primes p and q, then H is trivial; that is, H is either a group algebra or the dual of a group algebra. w x 2 w x Previously known cases include dimension 2 p M1 , dimension p M2 , w x and dimensions 3 p, 5p, and 7p GW . Westreich and the second author also obtained the same result for H, which is, along with its dual H U , of Ε½ Frobenius type i.e., the dimensions of their irreducible representations . w x divide the dimension of H GW, Theorem 3.5 . They concluded with the conjecture that any semisimple Hopf algebra H of dimension pq over k is trivial.

w x U

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