## 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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*On the action of Steenrod squares on polynomial algebras*II, J. Pure Appl. Algebra (to appear).

## 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