Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology

Authors:
David J. Pengelley and Frank Williams

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

Published electronically:
September 9, 1999

MathSciNet review:
1653375

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Abstract | References | Similar Articles | Additional Information

Abstract: The mod 2 Steenrod algebra and Dyer-Lashof algebra 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 , whose module actions are equivalent to, but quite different from, those of and . The exact relationships emerge as ``sheared algebra bijections'', which also illuminate the role of the cohomology of . As a bialgebra, has a particularly attractive and potentially useful structure, providing a bridge between those of and , and suggesting possible applications to the Miller spectral sequence and the structure of Dickson algebras.

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Additional Information

**David J. Pengelley**

Affiliation:
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003

Email:
davidp@nmsu.edu

**Frank Williams**

Affiliation:
Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003

Email:
frank@nmsu.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02468-X

Keywords:
Steenrod algebra,
Dyer-Lashof algebra,
bialgebras,
sheared algebra map,
Kudo-Araki-May algebra,
Nishida relations

Received by editor(s):
December 2, 1997

Published electronically:
September 9, 1999

Article copyright:
© Copyright 2000
American Mathematical Society