On the classification of finite-dimensional pointed Hopf algebras

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.

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      MRCLASS = {17B37 (16W35)},
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      MRREVIEWER = {Anthony Joseph},
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      ZBLNUMBER = {0822.16036},
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Authors

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