Pointed Hopf algebras are free over Hopf subalgebras
β Scribed by David E Radford
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 439 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
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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
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 β¬ a s a m a, β¬ x s x m a q 1 m x, and xa s qax Ε½ . Ε½ . for some q g k \_ 0. With the advent of quantum groups these re