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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hit polynomials and the canonical antiautomorphism of the Steenrod algebra
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by Judith H. Silverman PDF
Proc. Amer. Math. Soc. 123 (1995), 627-637 Request permission

Abstract:

In this paper, we generalize a formula of Davis (Proc. Amer. Math. Soc. 44 (1974), 235-236) for the antiautomorphism of the $\bmod \text {-}2$ Steenrod algebra $\mathcal {A}(2)$, in the process formulating the analogue of the Adem relations for products $Sq(\overbrace {0, \ldots ,0}^{t - 1},a) \cdot Sq(\overbrace {0, \ldots ,0}^{t - 1},b)$. We also state a generalization of a conjecture by the author and Singer (On the action of Steenrod squares on polynomial algebras II, J. Pure Appl. Algebra (to appear)) concerning the $\mathcal {A}(2)$-action on ${\mathbb {F}_2}[{x_1}, \ldots ,{x_s}]$ and use the antiautomorphism formula to prove several cases of the generalized conjecture. We discuss the relationship between the two conjectures and make explicit a sufficient condition for Monks’s work to prove a special case of the original conjecture. Finally, we illustrate in a table the relative strengths of the special cases of the conjectures known to be true.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 627-637
  • MSC: Primary 55S10; Secondary 20J05, 55R40
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1254854-8
  • MathSciNet review: 1254854