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.
-
[AS1]
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AUTHOR = {Andruskiewitsch, N. and Schneider, H.-J.},
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@incollection{AS3,
author = {Andruskiewitsch, N. and Schneider, H.-J.},
TITLE={Lifting of Nichols algebras of type $A_2$ and Pointed Hopf Algebras of order $ p^4$},
BOOKTITLE={Hopf Algebras and Quantum Groups},
VENUE={Brussels, 1998},
EDITOR={S. Caenepeel and F. van Oystaeyen},
SERIES={Lect. Notes in Pure and Appl. Math.},
VOLUME={209},
PAGES={1--14},
PUBLISHER={Dekker},
ADDRESS={New York},
YEAR={2000},
MRNUMBER={2001f:16069},
ZBLNUMBER={1020.16022},
} -
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Full Article