2011.111: Endomorphisms of the Steenrod algebra and of its odd subalgebra

2011.111: Robert Sandling (2011) Endomorphisms of the Steenrod algebra and of its odd subalgebra.

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Abstract

We characterise those algebra endomorphisms of the Steenrod algebra over the field of two elements, and those of its odd subalgebra, which send Steenrod squares to Steenrod squares or to 0. Two such maps appear in the literature, an epimorphism of the Steenrod algebra in the book of Steenrod and Epstein which halves superscripts on Steenrod squares and a monomorphism of the odd subalgebra in a paper of Monks. In the latter context a new map, an epimorphism, arises which has contrasting features to those of the endomorphism of Monks. Formulae for the endomorphisms are indicated both for the admissible and the Milnor bases.

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