Constructing Sequences of Divided Powers

Kenneth Newman
1972 Proceedings of the American Mathematical Society  
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,
more » ... 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.
doi:10.2307/2038507 fatcat:xyc6kwzv65hxxe3xrrpfx3iji4