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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a coradical of a finite-dimensional Hopf algebra


Author: David E. Radford
Journal: Proc. Amer. Math. Soc. 53 (1975), 9-15
MSC: Primary 16A24
DOI: https://doi.org/10.1090/S0002-9939-1975-0396652-0
MathSciNet review: 0396652
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Abstract: Examples are constructed showing that the coradical of a finite-dimensional Hopf algebra over any algebraically closed field is not necessarily a subalgebra (hence the Jacobson radical is not a Hopf ideal in general). The square of the antipode may induce a permutation on the simple subcoalgebras of dimension $ > 1$ of arbitrarily high order.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0396652-0
Keywords: Hopf algebra, Jacobson radical, order of antipode on coradical
Article copyright: © Copyright 1975 American Mathematical Society