Geodesic
On the classification of finite-dimensional pointed Hopf algebras
Nicolás Andruskiewitsch 1 ; Hans-Jürgen Schneider 2
1 Facultad de Matemática, Astronomía y física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
2 Mathematisches Institut, Universität München, Theresienstr. 39, D-80333 München, Germany
Annals of mathematics, Tome 171 (2010) no. 1, pp. 375-417

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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.

DOI : 10.4007/annals.2010.171.375

Nicolás Andruskiewitsch  1 ; Hans-Jürgen Schneider  2

1 Facultad de Matemática, Astronomía y física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
2 Mathematisches Institut, Universität München, Theresienstr. 39, D-80333 München, Germany 
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Nicolás Andruskiewitsch ; Hans-Jürgen Schneider . On the classification of finite-dimensional pointed Hopf algebras. Annals of mathematics, Tome 171 (2010) no. 1, pp. 375-417. doi: 10.4007/annals.2010.171.375

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