Constructing sequences of divided powers

Author:
Kenneth Newman

Journal:
Proc. Amer. Math. Soc. **31** (1972), 32-38

DOI:
https://doi.org/10.1090/S0002-9939-1972-0289606-3

MathSciNet review:
0289606

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Abstract | References | Additional Information

Abstract: In my *Sequences of divided powers in irreducible, cocommutative Hopf algebras*, I demonstrated the existence of extensions of sequences of divided powers over arbitrary fields, if certain coheight conditions are met. Here, I show that if the characteristic of the field does not divide , every sequence of divided powers of length , in a cocommutative Hopf algebra, has an extension that can be written as a polynomial in the previous terms. (An algorithm for finding these polynomials is given, together with a list of some of them.) Furthermore, I show that if one uses this method successively for constructing a sequence of divided powers over a primitive, the only obstructions will occur at powers of the characteristic of the field.

**[1]**K. Newman,*Sequences of divided powers in irreducible, cocommutative Hopf algebras*, Trans. Amer. Math. Soc.**163**(1971), 25-34. MR**0292875 (45:1957)****[2]**-,*Topics in the theory of irreducible Hopf algebras*, Ph.D. Thesis, Cornell University, Ithaca, New York, 1970.**[3]**M. E. Sweedler,*Hopf algebras*, Math. Lecture Note Series, Benjamin, New York, 1969. MR**40**#5705. MR**0252485 (40:5705)**

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0289606-3

Keywords:
Coheight,
irreducible Hopf algebra,
sequence of divided powers

Article copyright:
© Copyright 1972
American Mathematical Society