On pointed Hopf algebras of dimension 𝑝ⁿ

Beattie, M.; Dăscălescu, S.; Grünenfelder, L.

doi:10.1090/S0002-9939-99-04996-5

On pointed Hopf algebras of dimension $p^n$
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by M. Beattie, S. Dăscălescu and L. Grünenfelder

Proc. Amer. Math. Soc. 128 (2000), 361-367

DOI: https://doi.org/10.1090/S0002-9939-99-04996-5

Published electronically: July 6, 1999

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Abstract:

In this note we describe nonsemisimple Hopf algebras of dimension $p^n$ with coradical isomorphic to $kC$, $C$ abelian of order $p^{n-1}$, over an algebraically closed field $k$ of characteristic zero. If $C$ is cyclic or $C=(C_p)^{n-1}$, then we also determine the number of isomorphism classes of such Hopf algebras.

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