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Pointed Hopf algebras of dimension 32

Matias Graña
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Abstract

We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with characteristic different from 2. It turns out that there are infinite families of isomorphism classes of pointed Hopf algebras of dimension 32. In [Andruskiewitsch-Schneider, J. Alg 209], [Beattie-Dascalescu-Grunenfelder, Invent. Math. 136 (1)] and [Gelaki, J. Alg 209] are given families of counterexamples for the tenth Kaplansky conjecture. Up to now, 32 is the lowest dimension where Kaplansky conjecture fails.

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Matias Graña. 2001-10-02. Pointed Hopf algebras of dimension 32. https://arxiv.org/abs/math/0110033

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