Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Subalgebras of the $\mathbb{Z}/2$-equivariant Steenrod algebra

Pages: 281 – 305

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n1.a14

Author

Nicolas Ricka (Institut de Recherche Mathématique Avancée, UMR 7501, Strasbourg, France)

Abstract

The aim of this paper is to study subalgebras of the $\mathbb{Z}/2$- equivariant Steenrod algebra (for cohomology with coefficients in the constant Mackey functor $\underline{\mathbb{F}_2}$) that come from quotient Hopf algebroids of the $\mathbb{Z}/2$-equivariant dual Steenrod algebra. In particular, we study the equivariant counterpart of profile functions, exhibit the equivariant analogues of the classical $\mathcal{A}(n)$ and $\mathcal{E}(n)$, and show that the Steenrod algebra is free as a module over these.

Keywords

cohomology operation, Hopf algebroid, equivariant Steenrod algebra

2010 Mathematics Subject Classification

55S10, 55S91

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Published 18 May 2015