The main aim of this paper is to classify all types of Hopf algebras of dimension less thn or equal to 11 over an algebraically closed field of characteristic 0. If A is such a Hopf algebra that is not semisimple, then we shall prove that A or A\* is pointed. This property will result from the fact
A Survey of Hopf Algebras of Low Dimension
β Scribed by Margaret Beattie
- Publisher
- Springer Netherlands
- Year
- 2008
- Tongue
- English
- Weight
- 366 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0167-8019
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π SIMILAR VOLUMES
We show that if A is a semisimple Hopf algebra of dimension pq 2 over an algebraically closed field k of characteristic zero, then under certain restrictions either A or A \* must have a non-trivial central group-like element. We then classify all semisimple Hopf algebras of dimension pq 2 over k wh
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 tha
In this paper we completely classify nontrivial semisimple Hopf algebras of dimension 16. We also compute all the possible structures of the Grothendieck ring of semisimple non-commutative Hopf algebras of dimension 16. Moreover, we prove that non-commutative semisimple Hopf algebras of dimension p