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arXiv · math/9801130

On pointed Hopf algebras and Kaplansky's 10th conjecture

Shlomo Gelaki
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Abstract

In this paper we construct and study two new families of finite dimensional pointed Hopf algebras which generalize Radford's families. We show that over any infinite field which contains a primitive nth root of unity, one of the families contains infinitely many non-isomorphic Hopf algebras of any dimension of the form Nn^2, where 2<n<N are integers so that n divides N. We thus answer in the negative Kaplansky's 10th conjecture from 1975 on the finite number of types of Hopf algebras of a given dimension.

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BibTeXRIS

Shlomo Gelaki. 1998-06-29. On pointed Hopf algebras and Kaplansky's 10th conjecture. https://arxiv.org/abs/math/9801130

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