On the classification of finite-dimensional pointed Hopf algebras


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.


Nicolás Andruskiewitsch

Facultad de Matemática, Astronomía y física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina

Hans-Jürgen Schneider

Mathematisches Institut, Universität München, Theresienstr. 39, D-80333 München, Germany