On quadratic coalgebras, duality and the universal Steenrod algebra
Geoffrey Powell
TL;DR
This paper develops the concept of quadratic self-duality for coalgebras and applies it to algebraic structures in topology, providing a unified framework for understanding the universal Steenrod algebra and related results.
Contribution
It introduces quadratic self-duality for coalgebras and connects it to the universal Steenrod algebra, unifying previous results in algebraic topology.
Findings
Quadratic self-duality for coalgebras is established.
A unified framework for the universal Steenrod algebra is provided.
Connections to results of Lomonaco and Singer are clarified.
Abstract
The notion of quadratic self-duality for coalgebras is developed with applications to algebraic structures which arise naturally in algebraic topology, related to the universal Steenrod algebra via an appropriate form of duality. This explains and unifies results of Lomonaco and Singer.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra