TL;DR
This paper investigates the action of the Steenrod square Sq on the cohomology of the Steenrod algebra through the endomorphism Theta of the Lambda algebra, revealing injectivity properties and computing the kernel on the 4-line.
Contribution
It introduces a detailed analysis of Theta's behavior to understand Sq's action, including proving injectivity in low filtrations and computing the kernel on the 4-line.
Findings
Sq is injective in filtrations less than 4
Kernel of Sq on the 4-line is explicitly computed
Provides new insights into the structure of the Lambda algebra
Abstract
The action of Sq on the cohomology of the Steenrod algebra is induced by an endomorphism Theta of the Lambda algebra. This paper studies the behavior of Theta in order to understand the action of Sq; the main result is that Sq is injective in filtrations less than 4, and its kernel on the 4-line is computed.
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