A class of left ideals of the Steenrod algebra

I. Johnson and J. L. Merzel

We study the nested collection of left ideals of A, the mod 2 Steenrod algebra, L(k):=A{Sq^2⁰, Sq^2¹, Sq^2², ..., Sq^{2^k}}. We determine the smallest k such that Sqⁿ ∈ 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.

Homology, Homotopy and Applications, Vol. 9 (2007), No. 1, pp.185-191.

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