Polynomials and the mod 2 Steenrod Algebra
Volume 1. The Peterson Hit Problem
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: Available
 format: Paperback
 isbn: 9781108414487
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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 graduatelevel textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Read more Algebraic and combinatorial treatment accessible to those without a background in topology
 Largely selfcontained with detailed proofs
 Volume 1 is suitable for use as a graduatelevel text
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×Product details
 Date Published: November 2017
 format: Paperback
 isbn: 9781108414487
 length: 370 pages
 dimensions: 234 x 164 x 22 mm
 weight: 0.56kg
 availability: Available
Table of Contents
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 2dominance 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.
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