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Proceedings of the American Mathematical Society

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

 

 

Conjugation and excess in the Steenrod algebra


Author: Judith H. Silverman
Journal: Proc. Amer. Math. Soc. 119 (1993), 657-661
MSC: Primary 55S10
MathSciNet review: 1152292
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Abstract: In this paper we prove a formula involving the canonical antiautomorphism $ \chi $ of the $ \bmod {\text{-}}2$ Steenrod algebra $ \mathcal{A}(2)$, namely,

\begin{displaymath}\begin{array}{*{20}{c}} {\chi (S{q^{{2^j}({2^{i + 1}} - 1)}}S... ... + 1}} - 1)}} \cdots S{q^{({2^{j + 1}} - 1)}},} \\ \end{array} \end{displaymath}

and discuss its implications for the study of the image of the $ \mathcal{A}(2)$-action on $ {\mathbb{F}_2}[{x_1}, \cdots ,{x_s}]$.

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DOI: https://doi.org/10.1090/S0002-9939-1993-1152292-8
Keywords: Steenrod algebra, canonical automorphism, excess, Steenrod algebra action on polynomial algebra
Article copyright: © Copyright 1993 American Mathematical Society