Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology
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- by David J. Pengelley and Frank Williams PDF
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Abstract:
The mod 2 Steenrod algebra $\mathcal {A}$ and Dyer-Lashof algebra $\mathcal {R}$ have both striking similarities and differences arising from their common origins in “lower-indexed” algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra $\mathcal {K}$, whose module actions are equivalent to, but quite different from, those of $\mathcal {A}$ and $\mathcal {R}$. The exact relationships emerge as “sheared algebra bijections”, which also illuminate the role of the cohomology of $\mathcal {K}$. As a bialgebra, $\mathcal {K}^{*}$ has a particularly attractive and potentially useful structure, providing a bridge between those of $\mathcal {A^{*}}$ and $\mathcal {R^{*}}$, and suggesting possible applications to the Miller spectral sequence and the $\mathcal {A}$ structure of Dickson algebras.References
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Additional Information
- David J. Pengelley
- Affiliation: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003
- MR Author ID: 212080
- Email: davidp@nmsu.edu
- Frank Williams
- Affiliation: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003
- Email: frank@nmsu.edu
- Received by editor(s): December 2, 1997
- Published electronically: September 9, 1999
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 1453-1492
- MSC (1991): Primary 55S99; Secondary 16W30, 16W50, 55S10, 55S12, 57T05
- DOI: https://doi.org/10.1090/S0002-9947-99-02468-X
- MathSciNet review: 1653375