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

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

MathSciNet review:
0376742

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An example is given to show that the antipode of a finite dimensional Hopf algebra over a field of prime characteristic need not be semisimple. (For examples were previously known.) The example is a pointed irreducible Hopf algebra (with antipode ) of dimension such that .

**[1]**Nathan Jacobson,*Lie algebras*, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR**0143793****[2]**Richard Gustavus Larson,*Orders in Hopf algebras*, J. Algebra**22**(1972), 201–210. MR**0299658**, https://doi.org/10.1016/0021-8693(72)90140-8**[3]**David E. Radford,*A free rank 4 Hopf algebra with antipode of order 4*, Proc. Amer. Math. Soc.**30**(1971), 55–58. MR**0279161**, https://doi.org/10.1090/S0002-9939-1971-0279161-5**[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**0407069**, https://doi.org/10.2307/2373888**[5]**Moss E. Sweedler,*Hopf algebras*, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR**0252485****[6]**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****[7]**Earl J. Taft and Robert Lee Wilson,*On antipodes in pointed Hopf algebras*, J. Algebra**29**(1974), 27–32. MR**0338053**, https://doi.org/10.1016/0021-8693(74)90107-0

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
16A24

Retrieve articles in all journals with MSC: 16A24

Additional Information

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

Article copyright:
© Copyright 1975
American Mathematical Society