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Non-semisimple Hopf algebras of dimension p2

✍ Scribed by Siu-Hung Ng

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 127 KB
Volume: 255
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00139-4

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✦ Synopsis

Let H be a finite-dimensional Hopf algebra with antipode S of dimension pq over an algebraically closed field of characteristic 0, where p q are odd primes. If H is not semisimple, then the order of S 4 is p, and Tr(S 2p ) is an integer divisible by p 2 . In particular, if dim H = p 2 , we prove that H is isomorphic to a Taft algebra. This completes the classification for the Hopf algebras of dimension p 2 .

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