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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Hopf algebras with nonsemisimple antipode


Authors: Earl J. Taft and Robert Lee Wilson
Journal: Proc. Amer. Math. Soc. 49 (1975), 269-276
MSC: Primary 16A24
MathSciNet review: 0376742
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0376742-9
PII: S 0002-9939(1975)0376742-9
Article copyright: © Copyright 1975 American Mathematical Society