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A free rank $ 4$ Hopf algebra with antipode of order $ 4$


Author: David E. Radford
Journal: Proc. Amer. Math. Soc. 30 (1971), 55-58
MSC: Primary 18.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0279161-5
MathSciNet review: 0279161
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Abstract: Let k be an arbitrary commutative ring. In this paper we construct a free rank 4 Hopf algebra H over k with antipode of order 4 and also discuss its symmetry. H is not semisimple.


References [Enhancements On Off] (What's this?)

  • [1] R. Heyneman and M. E. Sweedler, Affine Hopf algebras. I, J. Algebra 13 (1969), 192-241. MR 39 #6876. MR 0245570 (39:6876)
  • [2] R. G. Larson, The order of the antipode of a Hopf algebra, Proc. Amer. Math. Soc. 21 (1969), 167-170. MR 39 #1524. MR 0240170 (39:1524)
  • [3] M. E. Sweedler, Hopf algebras, Math. Lecture Note Series, Benjamin, New York, 1969. MR 40 #5705. MR 0252485 (40:5705)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0279161-5
Keywords: Hopf algebra, antipode of Hopf algebra, free algebra, order of antipode
Article copyright: © Copyright 1971 American Mathematical Society

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