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# Homology, Homotopy and Applications

## Volume 9 (2007)

### Number 1

### A class of left ideals of the Steenrod algebra

Pages: 185 – 191

DOI: http://dx.doi.org/10.4310/HHA.2007.v9.n1.a7

#### Authors

#### Abstract

We study the nested collection of left ideals of $\mathcal{A}$, the mod 2 Steenrod algebra, $L(k) := \mathcal{A} \{\mathit{Sq}^{2^0}, \mathit{Sq}^{2^1}, \mathit{Sq}^{2^2}, \dots, \mathit{Sq}^{2^k}\}$. We determine the smallest $k$ such that $\mathit{Sq}^n \in L(k)$. We discuss an application which improves upon the results of F. R. Cohen and the first author in their paper comparing the loop of the degree 2 map on a sphere and the H-space squaring map on the loop of a sphere.

#### Keywords

Steenrod algebra; homotopy

#### 2010 Mathematics Subject Classification

55S10