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 of arbitrarily high order.

**[1]**Serge Lang,*Algebra*, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR**0197234****[2]**Richard Gustavus Larson,*Characters of Hopf algebras*, J. Algebra**17**(1971), 352–368. MR**0283054**, https://doi.org/10.1016/0021-8693(71)90018-4**[3]**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**0407069**, https://doi.org/10.2307/2373888**[4]**Moss E. Sweedler,*Hopf algebras*, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR**0252485****[5]**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**0286868****[6]**-,*Some finite dimensional pointed Hopf algebras with non-semisimple antipode*, Proc. Amer. Math. Soc. (to appear).

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Additional Information

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