On the classification of finite-dimensional pointed Hopf algebras

N. Andruskiewitsch; H. -J. Schneider

On the classification of finite-dimensional pointed Hopf algebras

Quantum Algebra 2010-06-29 v3

Authors: N. Andruskiewitsch , H. -J. Schneider

Abstract

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.

Keywords

pointed hopf algebras finite-dimensional group-like elements generalized small quantum groups deformations classification

Cite

@article{arxiv.math/0502157,
  title  = {On the classification of finite-dimensional pointed Hopf algebras},
  author = {N. Andruskiewitsch and H. -J. Schneider},
  journal= {arXiv preprint arXiv:math/0502157},
  year   = {2010}
}

Comments

38 pages. The determination of all isomorphisms between the Hopf algebras presented here is given. The title is changed. Third version: several improvements on the exposition mainly following suggestions of the referee

On the classification of finite-dimensional pointed Hopf algebras

Abstract

Keywords

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