Subalgebras of the Z/2-equivariant Steenrod algebra

TL;DR

This paper investigates subalgebras of the $Z/2$-equivariant Steenrod algebra, focusing on quotient Hopf algebroids, and introduces equivariant analogues of classical subalgebras, showing their module freeness.

Contribution

It introduces equivariant analogues of classical Steenrod subalgebras and demonstrates their module freeness over the entire algebra.

Findings

Defined equivariant profile functions

Constructed equivariant $Z/2$-Steenrod subalgebras

Proved freeness of the algebra over these subalgebras

Abstract

The aim of this paper is to study sub-algebras of the $\mathbb{Z}/2$-equivariant Steenrod algebra (for cohomology with coefficients in the constant Mackey functor $\mathbb{F}_2$) which 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.