Hopf algebras with nonsemisimple antipode

Taft, Earl J.; Wilson, Robert Lee

doi:10.1090/S0002-9939-1975-0376742-9

Hopf algebras with nonsemisimple antipode
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by Earl J. Taft and Robert Lee Wilson

Proc. Amer. Math. Soc. 49 (1975), 269-276

DOI: https://doi.org/10.1090/S0002-9939-1975-0376742-9

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Abstract:

An example is given to show that the antipode of a finite dimensional Hopf algebra over a field of prime characteristic $p > 2$ need not be semisimple. (For $p = 2$ examples were previously known.) The example is a pointed irreducible Hopf algebra $H$ (with antipode $S$) of dimension ${p^3}$ such that ${S^{2p}} = I \ne {S^2}$.

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