Unlocking potential with the best learning and research solutions

I want this title to be available as an eBook

Polynomials and the mod 2 Steenrod Algebra
2 Paperback Volume Set

Part of London Mathematical Society Lecture Note Series

Authors:
Grant Walker, University of Manchester
Reginald M. W. Wood, University of Manchester

Date Published: November 2017
availability: Temporarily unavailable - available from June 2021
format: Multiple copy pack
isbn: 9781108414067

Rate & review

Multiple copy pack

Add to wishlist

Looking for an inspection copy?

This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact [email protected] providing details of the course you are teaching.

Description

Contents

Resources

Courses

About the Authors

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.
- Algebraic and combinatorial treatment of Steenrod algebra
- Accessible to those without a background in topology
- Largely self-contained with detailed proofs
Read more
Customer reviews

Not yet reviewed
Be the first to review

Log in to review

Review was not posted due to profanity
×

, create a review

(If you're not , sign out)

Please enter the right captcha value

Please enter a star rating.

Your review must be a minimum of 12 words.

How do you rate this item?

Reviews must contain at least 12 words about the product.

×

Product details
- Date Published: November 2017
- format: Multiple copy pack
- isbn: 9781108414067
- length: 700 pages
- dimensions: 227 x 152 x 43 mm
- weight: 1.12kg
- contains: 1 b/w illus.
- availability: Temporarily unavailable - available from June 2021
Table of Contents
Volume 1: 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
Volume 2: Preface
16. The action of GL(n) on flags
17. Irreducible F2GL(n)-modules
18. Idempotents and characters
19. Splitting P(n) as an A2-module
20. The algebraic group Ḡ(n)
21. Endomorphisms of P(n) over A2
22. The Steinberg summands of P(n)
23. The d-spike module J(n)
24. Partial flags and J(n)
25. The symmetric hit problem
26. The dual of the symmetric hit problem
27. The cyclic splitting of P(n)
28. The cyclic splitting of DP(n)
29. The 4-variable hit problem, I
30. The 4-variable hit problem, II
Bibliography
Index of Notation for Volume 2
Index for Volume 2
Index of Notation for Volume 1
Index for Volume 1.
Authors
Grant Walker, University of Manchester
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, University of Manchester
Reginald M. W. Wood was a Professor in the School of Mathematics at the University of Manchester before his retirement in 2005.