Some quotient Hopf algebras of the dual Steenrod algebra
Author:
J. H. Palmieri
Journal:
Trans. Amer. Math. Soc. 358 (2006), 671685
MSC (2000):
Primary 55S10, 18G15, 20E18, 20J06
Published electronically:
March 10, 2005
MathSciNet review:
2177035
Fulltext PDF Free Access
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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 torsionfree, 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 981954350
Email:
palmieri@math.washington.edu
DOI:
http://dx.doi.org/10.1090/S0002994705036378
PII:
S 00029947(05)036378
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
