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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: 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 $ n$, every sequence of divided powers of length $ n - 1$, 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.


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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