Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem

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Grant Walker (University of Manchester) Reginald M. W. Wood (University of Manchester)

Polynomials and the mod 2 Steenrod Algebra

Volume 1, The Peterson Hit Problem

Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester)

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English

Cambridge University Press
09 November 2017

Discrete mathematics; Algebra; Algebraic topology; Combinatorics & graph theory

Series: London Mathematical Society Lecture Note Series

This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.

By: Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 441
Dimensions: Height: 227mm, Width: 151mm, Spine: 22mm
Weight: 560g
ISBN: 9781108414487
ISBN 10: 1108414486
Series: London Mathematical Society Lecture Note Series
Pages: 370
Publication Date: 09 November 2017
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Preface; 1. Steenrod squares and the hit problem; 2. Conjugate Steenrod squares; 3. The Steenrod algebra A2; 4. Products and conjugation in A2; 5. Combinatorial structures; 6. The cohit module Q(n); 7. Bounds for dim Qd(n); 8. Special blocks and a basis for Q(3); 9. The dual of the hit problem; 10. K(3) and Q(3) as F2GL(3)-modules; 11. The dual of the Steenrod algebra; 12. Further structure of A2; 13. Stripping and nilpotence in A2; 14. The 2-dominance theorem; 15. Invariants and the hit problem; Bibliography; Index of Notation for Volume 1; Index for Volume 1; Index of Notation for Volume 2; Index for Volume 2.

Grant Walker was a senior lecturer in the School of Mathematics at the University of Manchester before his retirement in 2005. Reginald M. W. Wood was a Professor in the School of Mathematics at the University of Manchester before his retirement in 2005.