Some quotient Hopf algebras of the dual Steenrod algebra

Author:
J. H. Palmieri

Journal:
Trans. Amer. Math. Soc. **358** (2006), 671-685

MSC (2000):
Primary 55S10, 18G15, 20E18, 20J06

DOI:
https://doi.org/10.1090/S0002-9947-05-03637-8

Published electronically:
March 10, 2005

MathSciNet review:
2177035

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Abstract: Fix a prime , and let be the polynomial part of the dual Steenrod algebra. The Frobenius map on induces the Steenrod operation on cohomology, and in this paper, we investigate this operation. We point out that if , then for any element in the cohomology of , if one applies enough times, the resulting element is nilpotent. We conjecture that the same is true at odd primes, and that ``enough times'' should be ``once.''

The bulk of the paper is a study of some quotients of in which the Frobenius is an isomorphism of order . We show that these quotients are dual to group algebras, the resulting groups are torsion-free, and hence every element in Ext over these quotients is nilpotent. We also try to relate these results to the questions about . The dual complete Steenrod algebra makes an appearance.

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Additional Information

**J. H. Palmieri**

Affiliation:
Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350

Email:
palmieri@math.washington.edu

DOI:
https://doi.org/10.1090/S0002-9947-05-03637-8

Received by editor(s):
January 7, 2003

Received by editor(s) in revised form:
February 19, 2004

Published electronically:
March 10, 2005

Article copyright:
© Copyright 2005
American Mathematical Society