On the classification of finite-dimensional pointed Hopf algebras

Details On the classification of finite-dimensional pointed Hopf algebras On the classification of finite-dimensional pointed Hopf algebras

2005-02-08

arxiv.org/abs/math/0502157v3

Ann. Math. Vol. 171 (2010), No. 1, 375-417

Mathematics

Quantum Algebra

38 pages. The determination of all isomorphisms between the Hopf algebras presented here is given. The title is changed. Third

Scientific paper

We classify finite-dimensional complex Hopf algebras $A$ which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements $G(A)$ is abelian such that all prime divisors of the order of $G(A)$ are $>7$. Since these Hopf algebras turn out to be deformations of a natural class of generalized small quantum groups, our result can be read as an axiomatic description of generalized small quantum groups.

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