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Polynomial modules over the Steenrod algebra and conjugation in the Milnor basis


Author: Kenneth G. Monks
Journal: Proc. Amer. Math. Soc. 122 (1994), 625-634
MSC: Primary 55S10; Secondary 20J06
DOI: https://doi.org/10.1090/S0002-9939-1994-1207540-3
MathSciNet review: 1207540
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Abstract: Let $ {P_s} = {\mathbb{F}_2}[{x_1}, \ldots ,{x_s}]$ be the $ \bmod\;2$ cohomology of the s-fold product of $ \mathbb{R}{{\text{P}}^\infty }$ with the usual structure as a module over the Steenrod algebra. A monomial in $ {P_s}$ is said to be hit if it is in the image of the action $ \bar A \otimes {P_s} \to {P_s}$ where $ \bar A$ is the augmentation ideal of A. We extend a result of Wood to determine a new family of hit monomials in $ {P_s}$. We then use similar methods to obtain a generalization of antiautomorphism formulas of Davis and Gallant.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1207540-3
Article copyright: © Copyright 1994 American Mathematical Society

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