On a coradical of a finite-dimensional Hopf algebra
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- by David E. Radford PDF
- Proc. Amer. Math. Soc. 53 (1975), 9-15 Request permission
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.References
- Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234
- Richard Gustavus Larson, Characters of Hopf algebras, J. Algebra 17 (1971), 352–368. MR 283054, DOI 10.1016/0021-8693(71)90018-4
- David E. Radford, The order of the antipode of a finite dimensional Hopf algebra is finite, Amer. J. Math. 98 (1976), no. 2, 333–355. MR 407069, DOI 10.2307/2373888
- Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
- Earl J. Taft, The order of the antipode of finite-dimensional Hopf algebra, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 2631–2633. MR 286868, DOI 10.1073/pnas.68.11.2631 —, Some finite dimensional pointed Hopf algebras with non-semisimple antipode, Proc. Amer. Math. Soc. (to appear).
Additional Information
- © Copyright 1975 American Mathematical Society
- 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