In his paper, ''On Kauffman's knot Invariants Arising from Finite w x Dimensional Hopf Algebras'' R1 , Radford constructed two extensive families of pointed Hopf algebras. The first one, denoted by H , n, q, N, generalizes Sweedler's well known 4-dimensional noncommutative and noncocommutative Hopf
Pointed Hopf Algebras—from Enveloping Algebras to
✍ Scribed by David E. Radford
- Publisher
- Springer Netherlands
- Year
- 2008
- Tongue
- English
- Weight
- 409 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0167-8019
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📜 SIMILAR VOLUMES
We give a structure theorem for pointed Hopf algebras of dimension p 3 , having coradical kC , where k is an algebraically closed field of characteristic zero. p Combining this with previous results, we obtain the complete classification of all pointed Hopf algebras of dimension p 3 .
Some of the first examples of Hopf algebras described over a field k w x which are neither commutative nor cocommutative 13, 14 involve elements a and x which satisfy the relations ⌬ a s a m a, ⌬ x s x m a q 1 m x, and xa s qax Ž . Ž . for some q g k \_ 0. With the advent of quantum groups these re